Acdream 1214 Nice Patterns Strike Back (矩阵乘法 + 状态压缩)

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Nice Patterns Strike Back

Time Limit: 4000/2000MS (Java/Others) Memory Limit: 128000/64000KB (Java/Others)

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Problem Description

      You might have noticed that there is the new fashion among rich people to have their yards tiled with black and white tiles, forming a pattern. The company Broken Tiles is well known as the best tiling company in our region. It provides the widest choices of nice patterns to tile your yard with. The pattern is nice if there is no square of size 2 × 2, such that all tiles in it have the same color. So patterns on the figure 1 are nice, while patterns on the figure 2 are not.

      The president of the company wonders whether the variety of nice patterns he can provide to the clients is large enough. Thus he asks you to find out the number of nice patterns that can be used to tile the yard of size N × M . Now he is interested in the long term estimation, so he suggests N ≤ 10100. However, he does not like big numbers, so he asks you to find the answer modulo P .

Input

      The input file contains three integer numbers: N (1 ≤ N ≤ 10100), M (1 ≤ M ≤ 5) and P (1 ≤ P ≤10000).

Output

      Write the number of nice patterns of size N × M modulo P to the output file.

Sample Input

2 2 5
3 3 23

Sample Output

4
0

Source

Andrew Stankevich Contest 1

题目大意：
给定一个 n*m 的矩阵 对于2*2的子方格若全是黑色或全是白色的是非法的，求出用黑色和白色两种颜色来涂这个矩阵的合法的方案数 (1<=n<=10^100, 1<=m<=5) 

解题思路：

首先 我们需要观察一下数据的范围，因为 m 最多只有5，也就是说最多有 5 列，那么最多有 2^5 个状态，那么我们可以构造出转移矩阵，上一行向下一行的转移矩阵，也就是最多32*32的矩阵A，在矩阵A中 如果上一行的i 状态可以向下一行的 j  状态 转移那么 A[i][j] = 1，否则 A[i][j] = 0，然后我们一共有 n  行，第一行默认为单位矩阵，那么A就是表示到达第二行的状态的方法数，然后 我们要求的就是 第 n 行的状态，也就是A^(n-1)，所以就是一个矩阵乘法，然后掺杂着大数（捡来一个大数模板 挺好用的），最后就是求一下所有的方法数的和也就是 A^(n-1)的和，状态(1<<kk)

（PS：Acdream 不支持 Java？？竟然提示 Dangerous Code/汗）

上代码：

#include <iostream>
#include <cstring>
#include <cstdio>
#include <cstdlib>
#include <algorithm>
using namespace std;

#define DIGIT   4      //四位隔开,即万进制
#define DEPTH   10000        //万进制
#define MAX     100+5    //题目最大位数/4，要不大直接设为最大位数也行
typedef int bignum_t[MAX+1];

/************************************************************************/
/* 读取操作数，对操作数进行处理存储在数组里                             */
/************************************************************************/
int read(bignum_t a,istream&is=cin)
{
    char buf[MAX*DIGIT+1],ch ;
    int i,j ;
    memset((void*)a,0,sizeof(bignum_t));
    if(!(is>>buf))return 0 ;
    for(a[0]=strlen(buf),i=a[0]/2-1; i>=0; i--)
        ch=buf[i],buf[i]=buf[a[0]-1-i],buf[a[0]-1-i]=ch ;
    for(a[0]=(a[0]+DIGIT-1)/DIGIT,j=strlen(buf); j<a[0]*DIGIT; buf[j++]='0');
    for(i=1; i<=a[0]; i++)
        for(a[i]=0,j=0; j<DIGIT; j++)
            a[i]=a[i]*10+buf[i*DIGIT-1-j]-'0' ;
    for(; !a[a[0]]&&a[0]>1; a[0]--);
    return 1 ;
}

void write(const bignum_t a,ostream&os=cout)
{
    int i,j ;
    for(os<<a[i=a[0]],i--; i; i--)
        for(j=DEPTH/10; j; j/=10)
            os<<a[i]/j%10 ;
}

int comp(const bignum_t a,const bignum_t b)
{
    int i ;
    if(a[0]!=b[0])
        return a[0]-b[0];
    for(i=a[0]; i; i--)
        if(a[i]!=b[i])
            return a[i]-b[i];
    return 0 ;
}

int comp(const bignum_t a,const int b)
{
    int c[12]=
    {
        1
    }
    ;
    for(c[1]=b; c[c[0]]>=DEPTH; c[c[0]+1]=c[c[0]]/DEPTH,c[c[0]]%=DEPTH,c[0]++);
    return comp(a,c);
}

int comp(const bignum_t a,const int c,const int d,const bignum_t b)
{
    int i,t=0,O=-DEPTH*2 ;
    if(b[0]-a[0]<d&&c)
        return 1 ;
    for(i=b[0]; i>d; i--)
    {
        t=t*DEPTH+a[i-d]*c-b[i];
        if(t>0)return 1 ;
        if(t<O)return 0 ;
    }
    for(i=d; i; i--)
    {
        t=t*DEPTH-b[i];
        if(t>0)return 1 ;
        if(t<O)return 0 ;
    }
    return t>0 ;
}
/************************************************************************/
/* 大数与大数相加                                                       */
/************************************************************************/
void add(bignum_t a,const bignum_t b)
{
    int i ;
    for(i=1; i<=b[0]; i++)
        if((a[i]+=b[i])>=DEPTH)
            a[i]-=DEPTH,a[i+1]++;
    if(b[0]>=a[0])
        a[0]=b[0];
    else
        for(; a[i]>=DEPTH&&i<a[0]; a[i]-=DEPTH,i++,a[i]++);
    a[0]+=(a[a[0]+1]>0);
}
/************************************************************************/
/* 大数与小数相加                                                       */
/************************************************************************/
void add(bignum_t a,const int b)
{
    int i=1 ;
    for(a[1]+=b; a[i]>=DEPTH&&i<a[0]; a[i+1]+=a[i]/DEPTH,a[i]%=DEPTH,i++);
    for(; a[a[0]]>=DEPTH; a[a[0]+1]=a[a[0]]/DEPTH,a[a[0]]%=DEPTH,a[0]++);
}
/************************************************************************/
/* 大数相减(被减数>=减数)                                               */
/************************************************************************/
void sub(bignum_t a,const bignum_t b)
{
    int i ;
    for(i=1; i<=b[0]; i++)
        if((a[i]-=b[i])<0)
            a[i+1]--,a[i]+=DEPTH ;
    for(; a[i]<0; a[i]+=DEPTH,i++,a[i]--);
    for(; !a[a[0]]&&a[0]>1; a[0]--);
}
/************************************************************************/
/* 大数减去小数(被减数>=减数)                                           */
/************************************************************************/
void sub(bignum_t a,const int b)
{
    int i=1 ;
    for(a[1]-=b; a[i]<0; a[i+1]+=(a[i]-DEPTH+1)/DEPTH,a[i]-=(a[i]-DEPTH+1)/DEPTH*DEPTH,i++);
    for(; !a[a[0]]&&a[0]>1; a[0]--);
}

void sub(bignum_t a,const bignum_t b,const int c,const int d)
{
    int i,O=b[0]+d ;
    for(i=1+d; i<=O; i++)
        if((a[i]-=b[i-d]*c)<0)
            a[i+1]+=(a[i]-DEPTH+1)/DEPTH,a[i]-=(a[i]-DEPTH+1)/DEPTH*DEPTH ;
    for(; a[i]<0; a[i+1]+=(a[i]-DEPTH+1)/DEPTH,a[i]-=(a[i]-DEPTH+1)/DEPTH*DEPTH,i++);
    for(; !a[a[0]]&&a[0]>1; a[0]--);
}
/************************************************************************/
/* 大数相乘，读入被乘数a，乘数b，结果保存在c[]                          */
/************************************************************************/
void mul(bignum_t c,const bignum_t a,const bignum_t b)
{
    int i,j ;
    memset((void*)c,0,sizeof(bignum_t));
    for(c[0]=a[0]+b[0]-1,i=1; i<=a[0]; i++)
        for(j=1; j<=b[0]; j++)
            if((c[i+j-1]+=a[i]*b[j])>=DEPTH)
                c[i+j]+=c[i+j-1]/DEPTH,c[i+j-1]%=DEPTH ;
    for(c[0]+=(c[c[0]+1]>0); !c[c[0]]&&c[0]>1; c[0]--);
}
/************************************************************************/
/* 大数乘以小数，读入被乘数a，乘数b，结果保存在被乘数                   */
/************************************************************************/
void mul(bignum_t a,const int b)
{
    int i ;
    for(a[1]*=b,i=2; i<=a[0]; i++)
    {
        a[i]*=b ;
        if(a[i-1]>=DEPTH)
            a[i]+=a[i-1]/DEPTH,a[i-1]%=DEPTH ;
    }
    for(; a[a[0]]>=DEPTH; a[a[0]+1]=a[a[0]]/DEPTH,a[a[0]]%=DEPTH,a[0]++);
    for(; !a[a[0]]&&a[0]>1; a[0]--);
}

void mul(bignum_t b,const bignum_t a,const int c,const int d)
{
    int i ;
    memset((void*)b,0,sizeof(bignum_t));
    for(b[0]=a[0]+d,i=d+1; i<=b[0]; i++)
        if((b[i]+=a[i-d]*c)>=DEPTH)
            b[i+1]+=b[i]/DEPTH,b[i]%=DEPTH ;
    for(; b[b[0]+1]; b[0]++,b[b[0]+1]=b[b[0]]/DEPTH,b[b[0]]%=DEPTH);
    for(; !b[b[0]]&&b[0]>1; b[0]--);
}
/**************************************************************************/
/* 大数相除,读入被除数a，除数b，结果保存在c[]数组                         */
/* 需要comp()函数                                                         */
/**************************************************************************/
void div(bignum_t c,bignum_t a,const bignum_t b)
{
    int h,l,m,i ;
    memset((void*)c,0,sizeof(bignum_t));
    c[0]=(b[0]<a[0]+1)?(a[0]-b[0]+2):1 ;
    for(i=c[0]; i; sub(a,b,c[i]=m,i-1),i--)
        for(h=DEPTH-1,l=0,m=(h+l+1)>>1; h>l; m=(h+l+1)>>1)
            if(comp(b,m,i-1,a))h=m-1 ;
            else l=m ;
    for(; !c[c[0]]&&c[0]>1; c[0]--);
    c[0]=c[0]>1?c[0]:1 ;
}

void div(bignum_t a,const int b,int&c)
{
    int i ;
    for(c=0,i=a[0]; i; c=c*DEPTH+a[i],a[i]=c/b,c%=b,i--);
    for(; !a[a[0]]&&a[0]>1; a[0]--);
}
/************************************************************************/
/* 大数平方根，读入大数a，结果保存在b[]数组里                           */
/* 需要comp()函数                                                       */
/************************************************************************/
void sqrt(bignum_t b,bignum_t a)
{
    int h,l,m,i ;
    memset((void*)b,0,sizeof(bignum_t));
    for(i=b[0]=(a[0]+1)>>1; i; sub(a,b,m,i-1),b[i]+=m,i--)
        for(h=DEPTH-1,l=0,b[i]=m=(h+l+1)>>1; h>l; b[i]=m=(h+l+1)>>1)
            if(comp(b,m,i-1,a))h=m-1 ;
            else l=m ;
    for(; !b[b[0]]&&b[0]>1; b[0]--);
    for(i=1; i<=b[0]; b[i++]>>=1);
}
/************************************************************************/
/* 返回大数的长度                                                       */
/************************************************************************/
int length(const bignum_t a)
{
    int t,ret ;
    for(ret=(a[0]-1)*DIGIT,t=a[a[0]]; t; t/=10,ret++);
    return ret>0?ret:1 ;
}
/************************************************************************/
/* 返回指定位置的数字，从低位开始数到第b位，返回b位上的数               */
/************************************************************************/
int digit(const bignum_t a,const int b)
{
    int i,ret ;
    for(ret=a[(b-1)/DIGIT+1],i=(b-1)%DIGIT; i; ret/=10,i--);
    return ret%10 ;
}
/************************************************************************/
/* 返回大数末尾0的个数                                                  */
/************************************************************************/
int zeronum(const bignum_t a)
{
    int ret,t ;
    for(ret=0; !a[ret+1]; ret++);
    for(t=a[ret+1],ret*=DIGIT; !(t%10); t/=10,ret++);
    return ret ;
}

void comp(int*a,const int l,const int h,const int d)
{
    int i,j,t ;
    for(i=l; i<=h; i++)
        for(t=i,j=2; t>1; j++)
            while(!(t%j))
                a[j]+=d,t/=j ;
}

void convert(int*a,const int h,bignum_t b)
{
    int i,j,t=1 ;
    memset(b,0,sizeof(bignum_t));
    for(b[0]=b[1]=1,i=2; i<=h; i++)
        if(a[i])
            for(j=a[i]; j; t*=i,j--)
                if(t*i>DEPTH)
                    mul(b,t),t=1 ;
    mul(b,t);
}
/************************************************************************/
/* 组合数                                                               */
/************************************************************************/
void combination(bignum_t a,int m,int n)
{
    int*t=new int[m+1];
    memset((void*)t,0,sizeof(int)*(m+1));
    comp(t,n+1,m,1);
    comp(t,2,m-n,-1);
    convert(t,m,a);
    delete[]t ;
}
/************************************************************************/
/* 排列数                                                               */
/************************************************************************/
void permutation(bignum_t a,int m,int n)
{
    int i,t=1 ;
    memset(a,0,sizeof(bignum_t));
    a[0]=a[1]=1 ;
    for(i=m-n+1; i<=m; t*=i++)
        if(t*i>DEPTH)
            mul(a,t),t=1 ;
    mul(a,t);
}

#define SGN(x) ((x)>0?1:((x)<0?-1:0))
#define ABS(x) ((x)>0?(x):-(x))

int read(bignum_t a,int&sgn,istream&is=cin)
{
    char str[MAX*DIGIT+2],ch,*buf ;
    int i,j ;
    memset((void*)a,0,sizeof(bignum_t));
    if(!(is>>str))return 0 ;
    buf=str,sgn=1 ;
    if(*buf=='-')sgn=-1,buf++;
    for(a[0]=strlen(buf),i=a[0]/2-1; i>=0; i--)
        ch=buf[i],buf[i]=buf[a[0]-1-i],buf[a[0]-1-i]=ch ;
    for(a[0]=(a[0]+DIGIT-1)/DIGIT,j=strlen(buf); j<a[0]*DIGIT; buf[j++]='0');
    for(i=1; i<=a[0]; i++)
        for(a[i]=0,j=0; j<DIGIT; j++)
            a[i]=a[i]*10+buf[i*DIGIT-1-j]-'0' ;
    for(; !a[a[0]]&&a[0]>1; a[0]--);
    if(a[0]==1&&!a[1])sgn=0 ;
    return 1 ;
}
struct bignum
{
    bignum_t num ;
    int sgn ;
public :
    inline bignum()
    {
        memset(num,0,sizeof(bignum_t));
        num[0]=1 ;
        sgn=0 ;
    }
    inline int operator!()
    {
        return num[0]==1&&!num[1];
    }
    inline bignum&operator=(const bignum&a)
    {
        memcpy(num,a.num,sizeof(bignum_t));
        sgn=a.sgn ;
        return*this ;
    }
    inline bignum&operator=(const int a)
    {
        memset(num,0,sizeof(bignum_t));
        num[0]=1 ;
        sgn=SGN (a);
        add(num,sgn*a);
        return*this ;
    }
    ;
    inline bignum&operator+=(const bignum&a)
    {
        if(sgn==a.sgn)add(num,a.num);
        else if
        (sgn&&a.sgn)
        {
            int ret=comp(num,a.num);
            if(ret>0)sub(num,a.num);
            else if(ret<0)
            {
                bignum_t t ;
                memcpy(t,num,sizeof(bignum_t));
                memcpy(num,a.num,sizeof(bignum_t));
                sub (num,t);
                sgn=a.sgn ;
            }
            else memset(num,0,sizeof(bignum_t)),num[0]=1,sgn=0 ;
        }
        else if(!sgn)
            memcpy(num,a.num,sizeof(bignum_t)),sgn=a.sgn ;
        return*this ;
    }
    inline bignum&operator+=(const int a)
    {
        if(sgn*a>0)add(num,ABS(a));
        else if(sgn&&a)
        {
            int  ret=comp(num,ABS(a));
            if(ret>0)sub(num,ABS(a));
            else if(ret<0)
            {
                bignum_t t ;
                memcpy(t,num,sizeof(bignum_t));
                memset(num,0,sizeof(bignum_t));
                num[0]=1 ;
                add(num,ABS (a));
                sgn=-sgn ;
                sub(num,t);
            }
            else memset(num,0,sizeof(bignum_t)),num[0]=1,sgn=0 ;
        }
        else if
        (!sgn)sgn=SGN(a),add(num,ABS(a));
        return*this ;
    }
    inline bignum operator+(const bignum&a)
    {
        bignum ret ;
        memcpy(ret.num,num,sizeof (bignum_t));
        ret.sgn=sgn ;
        ret+=a ;
        return ret ;
    }
    inline bignum operator+(const int a)
    {
        bignum ret ;
        memcpy(ret.num,num,sizeof (bignum_t));
        ret.sgn=sgn ;
        ret+=a ;
        return ret ;
    }
    inline bignum&operator-=(const bignum&a)
    {
        if(sgn*a.sgn<0)add(num,a.num);
        else if
        (sgn&&a.sgn)
        {
            int ret=comp(num,a.num);
            if(ret>0)sub(num,a.num);
            else if(ret<0)
            {
                bignum_t t ;
                memcpy(t,num,sizeof(bignum_t));
                memcpy(num,a.num,sizeof(bignum_t));
                sub(num,t);
                sgn=-sgn ;
            }
            else memset(num,0,sizeof(bignum_t)),num[0]=1,sgn=0 ;
        }
        else if(!sgn)add (num,a.num),sgn=-a.sgn ;
        return*this ;
    }
    inline bignum&operator-=(const int a)
    {
        if(sgn*a<0)add(num,ABS(a));
        else if(sgn&&a)
        {
            int  ret=comp(num,ABS(a));
            if(ret>0)sub(num,ABS(a));
            else if(ret<0)
            {
                bignum_t t ;
                memcpy(t,num,sizeof(bignum_t));
                memset(num,0,sizeof(bignum_t));
                num[0]=1 ;
                add(num,ABS(a));
                sub(num,t);
                sgn=-sgn ;
            }
            else memset(num,0,sizeof(bignum_t)),num[0]=1,sgn=0 ;
        }
        else if
        (!sgn)sgn=-SGN(a),add(num,ABS(a));
        return*this ;
    }
    inline bignum operator-(const bignum&a)
    {
        bignum ret ;
        memcpy(ret.num,num,sizeof(bignum_t));
        ret.sgn=sgn ;
        ret-=a ;
        return ret ;
    }
    inline bignum operator-(const int a)
    {
        bignum ret ;
        memcpy(ret.num,num,sizeof(bignum_t));
        ret.sgn=sgn ;
        ret-=a ;
        return ret ;
    }
    inline bignum&operator*=(const bignum&a)
    {
        bignum_t t ;
        mul(t,num,a.num);
        memcpy(num,t,sizeof(bignum_t));
        sgn*=a.sgn ;
        return*this ;
    }
    inline bignum&operator*=(const int a)
    {
        mul(num,ABS(a));
        sgn*=SGN(a);
        return*this ;
    }
    inline bignum operator*(const bignum&a)
    {
        bignum ret ;
        mul(ret.num,num,a.num);
        ret.sgn=sgn*a.sgn ;
        return ret ;
    }
    inline bignum operator*(const int a)
    {
        bignum ret ;
        memcpy(ret.num,num,sizeof (bignum_t));
        mul(ret.num,ABS(a));
        ret.sgn=sgn*SGN(a);
        return ret ;
    }
    inline bignum&operator/=(const bignum&a)
    {
        bignum_t t ;
        div(t,num,a.num);
        memcpy (num,t,sizeof(bignum_t));
        sgn=(num[0]==1&&!num[1])?0:sgn*a.sgn ;
        return*this ;
    }
    inline bignum&operator/=(const int a)
    {
        int t ;
        div(num,ABS(a),t);
        sgn=(num[0]==1&&!num [1])?0:sgn*SGN(a);
        return*this ;
    }
    inline bignum operator/(const bignum&a)
    {
        bignum ret ;
        bignum_t t ;
        memcpy(t,num,sizeof(bignum_t));
        div(ret.num,t,a.num);
        ret.sgn=(ret.num[0]==1&&!ret.num[1])?0:sgn*a.sgn ;
        return ret ;
    }
    inline bignum operator/(const int a)
    {
        bignum ret ;
        int t ;
        memcpy(ret.num,num,sizeof(bignum_t));
        div(ret.num,ABS(a),t);
        ret.sgn=(ret.num[0]==1&&!ret.num[1])?0:sgn*SGN(a);
        return ret ;
    }
    inline bignum&operator%=(const bignum&a)
    {
        bignum_t t ;
        div(t,num,a.num);
        if(num[0]==1&&!num[1])sgn=0 ;
        return*this ;
    }
    inline int operator%=(const int a)
    {
        int t ;
        div(num,ABS(a),t);
        memset(num,0,sizeof (bignum_t));
        num[0]=1 ;
        add(num,t);
        return t ;
    }
    inline bignum operator%(const bignum&a)
    {
        bignum ret ;
        bignum_t t ;
        memcpy(ret.num,num,sizeof(bignum_t));
        div(t,ret.num,a.num);
        ret.sgn=(ret.num[0]==1&&!ret.num [1])?0:sgn ;
        return ret ;
    }
    inline int operator%(const int a)
    {
        bignum ret ;
        int t ;
        memcpy(ret.num,num,sizeof(bignum_t));
        div(ret.num,ABS(a),t);
        memset(ret.num,0,sizeof(bignum_t));
        ret.num[0]=1 ;
        add(ret.num,t);
        return t ;
    }
    inline bignum&operator++()
    {
        *this+=1 ;
        return*this ;
    }
    inline bignum&operator--()
    {
        *this-=1 ;
        return*this ;
    }
    ;
    inline int operator>(const bignum&a)
    {
        return sgn>0?(a.sgn>0?comp(num,a.num)>0:1):(sgn<0?(a.sgn<0?comp(num,a.num)<0:0):a.sgn<0);
    }
    inline int operator>(const int a)
    {
        return sgn>0?(a>0?comp(num,a)>0:1):(sgn<0?(a<0?comp(num,-a)<0:0):a<0);
    }
    inline int operator>=(const bignum&a)
    {
        return sgn>0?(a.sgn>0?comp(num,a.num)>=0:1):(sgn<0?(a.sgn<0?comp(num,a.num)<=0:0):a.sgn<=0);
    }
    inline int operator>=(const int a)
    {
        return sgn>0?(a>0?comp(num,a)>=0:1):(sgn<0?(a<0?comp(num,-a)<=0:0):a<=0);
    }
    inline int operator<(const bignum&a)
    {
        return sgn<0?(a.sgn<0?comp(num,a.num)>0:1):(sgn>0?(a.sgn>0?comp(num,a.num)<0:0):a.sgn>0);
    }
    inline int operator<(const int a)
    {
        return sgn<0?(a<0?comp(num,-a)>0:1):(sgn>0?(a>0?comp(num,a)<0:0):a>0);
    }
    inline int operator<=(const bignum&a)
    {
        return sgn<0?(a.sgn<0?comp(num,a.num)>=0:1):(sgn>0?(a.sgn>0?comp(num,a.num)<=0:0):a.sgn>=0);
    }
    inline int operator<=(const int a)
    {
        return sgn<0?(a<0?comp(num,-a)>=0:1):
               (sgn>0?(a>0?comp(num,a)<=0:0):a>=0);
    }
    inline int operator==(const bignum&a)
    {
        return(sgn==a.sgn)?!comp(num,a.num):0 ;
    }
    inline int operator==(const int a)
    {
        return(sgn*a>=0)?!comp(num,ABS(a)):0 ;
    }
    inline int operator!=(const bignum&a)
    {
        return(sgn==a.sgn)?comp(num,a.num):1 ;
    }
    inline int operator!=(const int a)
    {
        return(sgn*a>=0)?comp(num,ABS(a)):1 ;
    }
    inline int operator[](const int a)
    {
        return digit(num,a);
    }
    friend inline istream&operator>>(istream&is,bignum&a)
    {
        read(a.num,a.sgn,is);
        return  is ;
    }
    friend inline ostream&operator<<(ostream&os,const bignum&a)
    {
        if(a.sgn<0)
            os<<'-' ;
        write(a.num,os);
        return os ;
    }
    friend inline bignum sqrt(const bignum&a)
    {
        bignum ret ;
        bignum_t t ;
        memcpy(t,a.num,sizeof(bignum_t));
        sqrt(ret.num,t);
        ret.sgn=ret.num[0]!=1||ret.num[1];
        return ret ;
    }
    friend inline bignum sqrt(const bignum&a,bignum&b)
    {
        bignum ret ;
        memcpy(b.num,a.num,sizeof(bignum_t));
        sqrt(ret.num,b.num);
        ret.sgn=ret.num[0]!=1||ret.num[1];
        b.sgn=b.num[0]!=1||ret.num[1];
        return ret ;
    }
    inline int length()
    {
        return :: length(num);
    }
    inline int zeronum()
    {
        return :: zeronum(num);
    }
    inline bignum C(const int m,const int n)
    {
        combination(num,m,n);
        sgn=1 ;
        return*this ;
    }
    inline bignum P(const int m,const int n)
    {
        permutation(num,m,n);
        sgn=1 ;
        return*this ;
    }
};

/**+++++++++++++++++++++++++++++++++++++++++++++++分界线+++++++++++++++++++++++++++++++++++++++++++++++++++++**/

const int MAXN = 35;
const int MAXM = 35;
int MOD;
int kk;
typedef struct
{
    int mat[MAXN][MAXM];
} Matrix;

Matrix Init()///单位矩阵
{
    Matrix I;
    for(int i=0; i<(1<<kk); i++)
    {
        for(int j=0; j<(1<<kk); j++)
        {
            if(i == j)
                I.mat[i][j] = 1;
            else
                I.mat[i][j] = 0;
        }
    }
    return I;
}
Matrix Multi_Matrix(Matrix a, Matrix b)///矩阵乘法
{
    Matrix c;
    for(int i=0; i<(1<<kk); i++)
    {
        for(int j=0; j<(1<<kk); j++)
        {
            c.mat[i][j] = 0;
            for(int k=0; k<(1<<kk); k++)
            {
                c.mat[i][j] += a.mat[i][k]*b.mat[k][j];
                c.mat[i][j] %= MOD;
            }
        }
    }
    return c;
}
int a[10];
bool Judge_get_Binary(int i, int j)///判断二进制状态
{
    int cnt1=0, cnt2=0;
    for(int k=0; k<kk; k++)
    {
        cnt1 = i%2;
        cnt2 = j%2;
        if(cnt1==1 && cnt2==1)
            a[k] = 1;
        else if(!cnt1 && !cnt2)
            a[k] = 0;
        else
            a[k] = -1;
        i/=2, j/=2;
    }
    for(int k=0; k<kk-1; k++)
    {
        if(a[k]==1 && a[k+1]==1)
            return 0;
        if(a[k]==0 && a[k+1]==0)
            return 0;
    }
    return 1;
}
Matrix BuildA()
{
    Matrix A;
    for(int i=0; i<(1<<kk); i++)
    {
        for(int j=0; j<(1<<kk); j++)
        {
            if(Judge_get_Binary(i, j))
                A.mat[i][j] = 1;
            else
                A.mat[i][j] = 0;
        }
    }
    return A;
}
Matrix quick_MOD_Matrix(bignum n)
{
    n = n-1;
    Matrix ans = Init();
    Matrix A = BuildA();
    while(n > 0)
    {
        if(n%2 == 1)
            ans = Multi_Matrix(ans, A);
        n /= 2;
        A = Multi_Matrix(A, A);
    }
    return ans;
}
int main()
{
    bignum n;
    while(cin>>n>>kk>>MOD)
    {
        Matrix ans = quick_MOD_Matrix(n);
        int sum = 0;
        for(int i=0; i<(1<<kk); i++)
        {
            for(int j=0; j<(1<<kk); j++)
            {
                sum = sum + ans.mat[i][j];
                sum %= MOD;
            }
        }
        sum = (sum%MOD+MOD)%MOD;
        cout<<sum<<endl;
    }
    return 0 ;
}
/**
2 2 5
3 3 23
**/