51nod 1643 小Q的家庭作业

                                            
  //File Name: nod1643.cpp
  //Author: long
  //Mail: 736726758@qq.com
  //Created Time: 2016年12月22日 星期四 17时15分27秒
                                   
#include <bits/stdc++.h>
#define LL long long
const int MAXN = 10000000 + 1;
const int N = 664579 + 1;
const int P = (int)1e9 + 7;
int fir[MAXN],prime[MAXN],num[MAXN];
LL g,m,x,a,b,c;
int tot,C;
LL qp(LL x,LL y){
    LL res = 1;
    for(;y>0;y>>=1){
        if(y & 1){
               res = res * x;
            if(res >= P)
                res %= P;
        }
        x = x * x;
        if(x >= P) x %= P;
    }
    return res;
}
void init(){
    memset(fir,-1,sizeof(fir));
    tot = 0;
    for(int i=2,j;i<MAXN;++i){
        if(fir[i] == -1){
            prime[tot++] = i;
            fir[i] = tot - 1;
        }
        for(j=0;j<tot;++j){
            if((LL)i * prime[j] >= MAXN) break;
            fir[i * prime[j]] = j;
            if(i % prime[j] == 0) break;
        }
    }
}
void cal_num(){
//    memset(prime,0,sizeof(prime));
    prime[x] = 1,num[x] = 1,fir[1] = x;
    C = x;
    g *= x;
    LL l = 0,r = 0,len = 1;
    for(LL i=2;i<=m;++i){
        x = (a * x + b) % c + 1;
        if(x > C) C = x;
//        printf("i = %d x = %lld\n",i,x);
        if(!prime[x]){
            ++num[x];
            prime[x] = i;
            fir[i] = x;
            g = g * x;
            if(g >= P) g %= P;
        }
        else{
            l = prime[x],r = i;
            len = r - l;
            break;
        }
    }
    if(r){
        int rest = (m - r + 1) % len + l - 1;
        LL dive = (m - r + 1) / len;
        LL u = 1,v = 1,w = dive % P,tmp;
        for(LL i=l,now;i<r;++i){
            now = w;
            v = fir[i];
            u = u * v;
            if(u >= P) u %= P;
            if(i <= rest){
                   ++now;
                g = g * v;
                if(g >= P) g %= P;
            }
            tmp = num[v] + now;
            if(tmp >= P) tmp -= P;
            num[v] = tmp;
        }
        g = g * qp(u,dive);
        if(g >= P) g %= P;
    }
}
void cal_sum(LL c){
    for(LL i=c,id,p,u;i>1;--i){
        if(!num[i]) continue;
        if(prime[fir[i]] == i){
            g = g * (num[i] + 1LL);
            if(g >= P) g %= P;
        }
        else{
            id = fir[i];
            p = prime[id];
            u = num[p] + num[i];
            if(u >= P) u -= P;
            num[p] = u;
            u = num[i / p] + num[i];
            if(u >= P) u -= P;
            num[i / p] = u;
        }
    }
}
void solve(){
    g = 1;
    cal_num();
    init();
    cal_sum(C);
}
int main(){
    scanf("%lld %lld %lld %lld %lld",&m,&x,&a,&b,&c);
    solve();
    printf("%lld\n",g);
    return 0;
}