bzoj3209 花神的数论题

题目链接：http://www.lydsy.com/JudgeOnline/problem.php?id=3209

题目大意：设sum(i)为i在二进制下的1的个数，求sum(1)~sum(n)的乘积模1e8+7的值。n< =1e15

题目分析：将n加1后，转为二进制，然后数位dp即可。

#include<cstdio>
#include<cstring>
#include<cstdlib>
#include<cmath>
#include<iostream>
#include<algorithm>

using namespace std;

typedef long long LL;
const LL mod=10000007;
LL C[300][300];
LL pow_mod(LL a,LL i)
{
	if (i==0) return 1%mod;
	LL temp=pow_mod(a,i>>1);
    temp=temp*temp%mod;
    if (i&1) temp=(LL) temp*a%mod;
    return temp;
}
LL a[2000],num=0;
LL solve(LL x)
{
	LL ans=0;
	for (int i=num;i>=1;i--)
	{
		if (a[i])
		{
			ans+=C[i-1][x];
			x--;
		}
		if (x<0) return ans;
	}
	return ans;
}
int main()
{
	LL n;
	cin>>n;
	n++;
	for (int i=0;i<60;i++)
	{
		C[i][0]=1;
		for (int j=1;j<=i;j++)
		    C[i][j]=C[i-1][j]+C[i-1][j-1];
	}
	LL ans=1;
	
	while (n>0)
	{
		a[++num]=n%2;
		n>>=1;
	}
	for (int i=1;i<=num;i++)
	    ans=ans*pow_mod(i,solve(i))%mod;
	cout<<ans<<endl;
	return 0;
}