#include <iostream>
#include <sstream>
#include <iomanip>
#include <vector>
#include <string>
#include <map>
#include <set>
#include <algorithm>
#include <numeric>
#include <iterator>
#include <functional>
#include <complex>
#include <queue>
#include <stack>
#include <cmath>
#include <cassert>
#include <tuple>
using namespace std;
typedef long long LL;
typedef complex<double> CMP;
static const unsigned MODVAL = 1000000007;
struct mint
{
unsigned val;
mint() :val(0) {}
mint(int x) :val(x%MODVAL) {}
mint(unsigned x) :val(x%MODVAL) {}
mint(LL x) :val(x%MODVAL) {}
};
mint& operator+=(mint& x, mint y) { return x = x.val + y.val; }
mint& operator-=(mint& x, mint y) { return x = x.val - y.val + MODVAL; }
mint& operator*=(mint& x, mint y) { return x = LL(x.val)*y.val; }
mint operator+(mint x, mint y) { return x += y; }
mint operator-(mint x, mint y) { return x -= y; }
mint operator*(mint x, mint y) { return x *= y; }
mint POW(mint x, LL e) { mint v = 1; for (; e; x *= x, e >>= 1) if (e & 1) v *= x; return v; }
mint& operator/=(mint& x, mint y) { return x *= POW(y, MODVAL - 2); }
mint operator/(mint x, mint y) { return x /= y; }
LL eulerPhi(LL n) {
LL ans = n;
for (LL x = 2; x*x <= n; ++x) {
if (n % x == 0) {
ans -= ans / x;
while (n % x == 0) n /= x;
}
}
if (n > 1) ans -= ans / n;
return ans;
}
class ModEquation { public:
vector <int> count(int n, int K, vector <int> query)
{
int epk = (int)eulerPhi(K);
vector<pair<int, int>> dK;
int v = K;
for (int p = 2; p*p <= v; ++p)
if (v%p == 0) {
int cnt = 0;
while (v%p == 0) cnt++, v /= p;
dK.emplace_back(p, cnt);
}
if (v != 1)
dK.emplace_back(v, 1);
vector<int> ans;
for (int q : query)
ans.push_back(solve(n, K, epk, dK, q).val);
return ans;
}
// # of solutions in mod K world s.t. x[0] x[1] ... x[n-1] = q
//
// * n <= 50
// * K = BIG
// * must be solved 1000 times in time limits.
mint solve(int n, int K, int epk, const vector<pair<int,int>>& dK, int q)
{
if (n == 1)
return 1;
mint ans = POW(epk, n-1);
for (auto pe : dK) {
int p = pe.first;
int e = pe.second;
int qq = q;
int cnt = 0;
while (qq%p == 0 && cnt<e)
cnt++, qq /= p;
// p^cnt is in gcd(K,q)
if (cnt < e) {
ans *= POW(n, cnt); // div dups...
}
else {
ans *= POW(n, cnt); // or more...
}
}
return ans;
}
};
// BEGIN CUT HERE
#include <ctime>
double start_time; string timer()
{ ostringstream os; os << " (" << int((clock()-start_time)/CLOCKS_PER_SEC*1000) << " msec)"; return os.str(); }
template<typename T> ostream& operator<<(ostream& os, const vector<T>& v)
{ os << "{ ";
for(typename vector<T>::const_iterator it=v.begin(); it!=v.end(); ++it)
os << '\"' << *it << '\"' << (it+1==v.end() ? "" : ", "); os << " }"; return os; }
void verify_case(const vector <int>& Expected, const vector <int>& Received) {
bool ok = (Expected == Received);
if(ok) cerr << "PASSED" << timer() << endl; else { cerr << "FAILED" << timer() << endl;
cerr << "\to: " << Expected << endl << "\tx: " << Received << endl; } }
#define CASE(N) {cerr << "Test Case #" << N << "..." << flush; start_time=clock();
#define END verify_case(_, ModEquation().count(n, K, query));}
int main(){
CASE(0)
int n = 2;
int K = 2;
int query_[] = {0,1};
vector <int> query(query_, query_+sizeof(query_)/sizeof(*query_));
int __[] = {3, 1 };
vector <int> _(__, __+sizeof(__)/sizeof(*__));
END
CASE(1)
int n = 2;
int K = 4;
int query_[] = {0,1,2,3};
vector <int> query(query_, query_+sizeof(query_)/sizeof(*query_));
int __[] = {8, 2, 4, 2 };
vector <int> _(__, __+sizeof(__)/sizeof(*__));
END
CASE(2)
int n = 6;
int K = 6;
int query_[] = {4};
vector <int> query(query_, query_+sizeof(query_)/sizeof(*query_));
int __[] = {2016 };
vector <int> _(__, __+sizeof(__)/sizeof(*__));
END
CASE(3)
int n = 1;
int K = 2;
int query_[] = {0,0,0,1,1,1};
vector <int> query(query_, query_+sizeof(query_)/sizeof(*query_));
int __[] = {1, 1, 1, 1, 1, 1 };
vector <int> _(__, __+sizeof(__)/sizeof(*__));
END
/*
CASE(4)
int n = ;
int K = ;
int query_[] = ;
vector <int> query(query_, query_+sizeof(query_)/sizeof(*query_));
int __[] = ;
vector <int> _(__, __+sizeof(__)/sizeof(*__));
END
CASE(5)
int n = ;
int K = ;
int query_[] = ;
vector <int> query(query_, query_+sizeof(query_)/sizeof(*query_));
int __[] = ;
vector <int> _(__, __+sizeof(__)/sizeof(*__));
END
*/
}
// END CUT HERE