构造矩阵，进行矩阵快速幂即可。。。
#include #include #include #include #include #include #include #include #include #include #include #include #include #define maxn 55 #define maxm 200005 #define eps 1e-10 #define mod 10000007 #define INF 1e9 #define lowbit(x) (x&(-x)) #define mp make_pair #define ls o<<1 #define rs o<<1 | 1 #define lson o<<1, L, mid #define rson o<<1 | 1, mid+1, R typedef long long LL; //typedef int LL; using namespace std; LL qpow(LL a, LL b){LL res=1,base=a;while(b){if(b%2)res=res*base;base=base*base;b/=2;}return res;} LL powmod(LL a, LL b){LL res=1,base=a;while(b){if(b%2)res=res*base%mod;base=base*base%mod;b/=2;}return res;} void scanf(int &__x){__x=0;char __ch=getchar();while(__ch==' '||__ch=='\n')__ch=getchar();while(__ch>='0'&&__ch<='9')__x=__x*10+__ch-'0',__ch = getchar();} LL gcd(LL _a, LL _b){if(!_b) return _a;else return gcd(_b, _a%_b);} // head int num[maxn], ans[maxn]; int mat[maxn][maxn], mid[maxn][maxn], res[maxn][maxn]; int n, m, t, tt; void init(void) { memset(mat, 0, sizeof mat); memset(res, 0, sizeof res); memset(ans, 0, sizeof ans); } void read(void) { t = n + 2; num[1] = 1, num[2] = 233; for(int i = 3; i <= t; i++) scanf("%d", &num[i]); } void calculate(void) { while(m) { if(m % 2) { for(int i = 1; i <= t; i++) for(int j = 1; j <= t; j++) { LL tmp = 0; for(int k = 1; k <= t; k++) tmp = (tmp + (LL)res[i][k] * mat[k][j]) % mod; mid[i][j] = tmp; } for(int i = 1; i <= t; i++) for(int j = 1; j <= t; j++) res[i][j] = mid[i][j]; } for(int i = 1; i <= t; i++) for(int j = 1; j <= t; j++) { LL tmp = 0; for(int k = 1; k <= t; k++) tmp = (tmp + (LL)mat[i][k] * mat[k][j]) % mod; mid[i][j] = tmp; } for(int i = 1; i <= t; i++) for(int j = 1; j <= t; j++) mat[i][j] = mid[i][j]; m /= 2; } } void work(void) { mat[1][1] = 1, mat[1][2] = 3, mat[2][2] = 10; for(int i = 3; i <= t; i++) for(int j = 2; j <= i; j++) mat[j][i] = 1; for(int i = 1; i <= t; i++) res[i][i] = 1; calculate(); for(int i = 1; i <= t; i++) for(int j = 1; j <= t; j++) ans[i] = ((LL)ans[i] + (LL)num[j] * res[j][i]) % mod; printf("%d\n", ans[t]); } int main(void) { while(scanf("%d%d", &n, &m)!=EOF) { init(); read(); work(); } return 0; }
