OJ-Problems-Source/QUSTOJ/1841_x7536110.cpp
2016-10-12 11:28:56 +08:00

84 lines
1.8 KiB
C++

#include <bits/stdc++.h>
using namespace std;
typedef long long LL;
const int N = 4;
struct mat {
LL c[N][N];
mat() { memset(c, 0, sizeof(c)); }
};
int T;
LL n, y, x, s, mod;
mat operator *(mat a, mat b) {
mat c;
for(int i = 0; i < N; i++)
for(int j = 0; j < N; j++)
for(int k = 0; k < N; k++) {
c.c[i][j] += a.c[i][k]*b.c[k][j];
if(c.c[i][j] >= mod) (c.c[i][j] %= mod) += mod;
}
return c;
}
mat operator ^(mat x, LL a) {
mat res;
for(int i = 0; i < N; i++) res.c[i][i] = 1;
while(a) {
if(a & 1) res = res * x;
x = x * x;
a >>= 1;
}
return res;
}
LL quick_mi(LL x, LL a) {
LL res = 1;
while(a) {
if(a & 1) res = res * x % mod;
x = x * x % mod;
a >>= 1;
}
return res;
}
LL phi(LL n) {
LL res = n;
for(LL i = 2, mx = sqrt(n+0.5); i <= mx; i++) {
if(n % i) continue;
res = res - res / i;
while(n % i == 0) n /= i;
}
if(n > 1) res = res - res / n;
return res;
}
int main() {
//freopen("in.txt", "r", stdin);
//freopen("out.txt", "w", stdout);
mat bb;
bb.c[0][0] = 1; bb.c[0][1] = 4; bb.c[0][2] = 1; bb.c[0][3] = 4;
bb.c[1][0] = 0; bb.c[1][1] = 4; bb.c[1][2] = 1; bb.c[1][3] = 4;
bb.c[2][0] = 0; bb.c[2][1] = 1; bb.c[2][2] = 0; bb.c[2][3] = 0;
bb.c[3][0] = 0; bb.c[3][1] = 2; bb.c[3][2] = 0; bb.c[3][3] = 1;
scanf("%d", &T);
while(T--) {
scanf("%lld%lld%lld%lld", &n, &y, &x, &s);
if(n == 0 || y == 0) {
puts("1");
continue;
}
mod = phi(s+1);
mat aa;
aa.c[0][0] = 1; aa.c[1][0] = 1; aa.c[2][0] = 0; aa.c[3][0] = 0;
aa = (bb^(n*y-1))*aa;
mod = s+1;
printf("%lld\n", quick_mi(x, aa.c[0][0]));
}
return 0;
}