HDU6395 分块思想

 传送门

#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
const int N=1e5+10;
const int mo=1e9+7;
ll n, P, F[N], C, D, inv[N];
struct Matrix{
    ll m[3][3];
};

void init(){
    F[1]%=mo; F[2]%=mo;
    for(int i=3; i<=1e5; i++)
        F[i]=(C*F[i-2]%mo+D*F[i-1]%mo+P/i)%mo;
}

inline void gouzao1(Matrix& tmp){
    memset(tmp.m, 0, sizeof tmp.m);
    tmp.m[1][0]=C; tmp.m[1][1]=D;
    tmp.m[0][1]=1;  tmp.m[2][2]=1;
}
inline void gouzao2(Matrix& tmp){
    memset(tmp.m, 0, sizeof tmp.m);
    tmp.m[0][0]=F[99998], tmp.m[1][0]=F[99999], tmp.m[2][0]=1;
}

inline Matrix Mul(Matrix& a, Matrix& b){
    Matrix c;
    for(int i=0; i<3; i++){
        for(int j=0; j<3; j++){
            c.m[i][j]=0;
            for(int k=0; k<3; k++)
                c.m[i][j]=(c.m[i][j]+a.m[i][k]*b.m[k][j]%mo)%mo;
        }
    }
    return c;
}

Matrix M_pow(Matrix bas, int m){
    Matrix ret;
    memset(ret.m, 0, sizeof ret.m);
    ret.m[0][0]=ret.m[1][1]=ret.m[2][2]=1;
    while(m){
        if(m&1)
            ret=Mul(ret, bas);
        m>>=1;
        bas=Mul(bas, bas);
    }
    return ret;
}

int main(){
    int T;
    scanf("%d", &T);
    while(T--){

        scanf("%lld%lld%lld%lld%lld%lld", &F[1], &F[2], &C, &D, &P, &n);
        init();
        if(n<=1e5)
            printf("%lld\n", F[n]);
        else{
            Matrix tmp, ans, tmp1;
            gouzao1(tmp); gouzao2(ans);
            for(int i=1e5, las; i<=n; i=las+1){
                las=P/i==0 ? n : min(P/(P/i), n); tmp.m[1][2]=P/i;

                tmp1=M_pow(tmp, las-i+1);
                ans=Mul(tmp1, ans);
            }
            printf("%lld\n", ans.m[1][0]);
        }
    }

    return 0;
}