f94ac98860 2016-12-29        kinaba: #include <iostream>
f94ac98860 2016-12-29        kinaba: #include <sstream>
f94ac98860 2016-12-29        kinaba: #include <iomanip>
f94ac98860 2016-12-29        kinaba: #include <vector>
f94ac98860 2016-12-29        kinaba: #include <string>
f94ac98860 2016-12-29        kinaba: #include <map>
f94ac98860 2016-12-29        kinaba: #include <set>
f94ac98860 2016-12-29        kinaba: #include <algorithm>
f94ac98860 2016-12-29        kinaba: #include <numeric>
f94ac98860 2016-12-29        kinaba: #include <iterator>
f94ac98860 2016-12-29        kinaba: #include <functional>
f94ac98860 2016-12-29        kinaba: #include <complex>
f94ac98860 2016-12-29        kinaba: #include <queue>
f94ac98860 2016-12-29        kinaba: #include <stack>
f94ac98860 2016-12-29        kinaba: #include <cmath>
f94ac98860 2016-12-29        kinaba: #include <cassert>
f94ac98860 2016-12-29        kinaba: #include <tuple>
f94ac98860 2016-12-29        kinaba: using namespace std;
f94ac98860 2016-12-29        kinaba: typedef long long LL;
f94ac98860 2016-12-29        kinaba: typedef complex<double> CMP;
f94ac98860 2016-12-29        kinaba: 
f94ac98860 2016-12-29        kinaba: static const unsigned MODVAL = 1000000007;
f94ac98860 2016-12-29        kinaba: struct mint
f94ac98860 2016-12-29        kinaba: {
f94ac98860 2016-12-29        kinaba: 	unsigned val;
f94ac98860 2016-12-29        kinaba: 	mint() :val(0) {}
f94ac98860 2016-12-29        kinaba: 	mint(int      x) :val(x%MODVAL) {}
f94ac98860 2016-12-29        kinaba: 	mint(unsigned x) :val(x%MODVAL) {}
f94ac98860 2016-12-29        kinaba: 	mint(LL       x) :val(x%MODVAL) {}
f94ac98860 2016-12-29        kinaba: };
f94ac98860 2016-12-29        kinaba: mint& operator+=(mint& x, mint y) { return x = x.val + y.val; }
f94ac98860 2016-12-29        kinaba: mint& operator-=(mint& x, mint y) { return x = x.val - y.val + MODVAL; }
f94ac98860 2016-12-29        kinaba: mint& operator*=(mint& x, mint y) { return x = LL(x.val)*y.val; }
f94ac98860 2016-12-29        kinaba: mint operator+(mint x, mint y) { return x += y; }
f94ac98860 2016-12-29        kinaba: mint operator-(mint x, mint y) { return x -= y; }
f94ac98860 2016-12-29        kinaba: mint operator*(mint x, mint y) { return x *= y; }
f94ac98860 2016-12-29        kinaba: 
f94ac98860 2016-12-29        kinaba: mint POW(mint x, LL e) { mint v = 1; for (; e; x *= x, e >>= 1) if (e & 1) v *= x; return v; }
f94ac98860 2016-12-29        kinaba: mint& operator/=(mint& x, mint y) { return x *= POW(y, MODVAL - 2); }
f94ac98860 2016-12-29        kinaba: mint operator/(mint x, mint y) { return x /= y; }
f94ac98860 2016-12-29        kinaba: 
f94ac98860 2016-12-29        kinaba: LL eulerPhi(LL n) {
f94ac98860 2016-12-29        kinaba: 	LL ans = n;
f94ac98860 2016-12-29        kinaba: 	for (LL x = 2; x*x <= n; ++x) {
f94ac98860 2016-12-29        kinaba: 		if (n % x == 0) {
f94ac98860 2016-12-29        kinaba: 			ans -= ans / x;
f94ac98860 2016-12-29        kinaba: 			while (n % x == 0) n /= x;
f94ac98860 2016-12-29        kinaba: 		}
f94ac98860 2016-12-29        kinaba: 	}
f94ac98860 2016-12-29        kinaba: 	if (n > 1) ans -= ans / n;
f94ac98860 2016-12-29        kinaba: 	return ans;
f94ac98860 2016-12-29        kinaba: }
f94ac98860 2016-12-29        kinaba: 
f94ac98860 2016-12-29        kinaba: class ModEquation { public:
f94ac98860 2016-12-29        kinaba: 	vector <int> count(int n, int K, vector <int> query)
f94ac98860 2016-12-29        kinaba: 	{
f94ac98860 2016-12-29        kinaba: 		int epk = (int)eulerPhi(K);
f94ac98860 2016-12-29        kinaba: 
f94ac98860 2016-12-29        kinaba: 		vector<pair<int, int>> dK;
f94ac98860 2016-12-29        kinaba: 		int v = K;
f94ac98860 2016-12-29        kinaba: 		for (int p = 2; p*p <= v; ++p)
f94ac98860 2016-12-29        kinaba: 			if (v%p == 0) {
f94ac98860 2016-12-29        kinaba: 				int cnt = 0;
f94ac98860 2016-12-29        kinaba: 				while (v%p == 0) cnt++, v /= p;
f94ac98860 2016-12-29        kinaba: 				dK.emplace_back(p, cnt);
f94ac98860 2016-12-29        kinaba: 			}
f94ac98860 2016-12-29        kinaba: 		if (v != 1)
f94ac98860 2016-12-29        kinaba: 			dK.emplace_back(v, 1);
f94ac98860 2016-12-29        kinaba: 
f94ac98860 2016-12-29        kinaba: 		vector<int> ans;
f94ac98860 2016-12-29        kinaba: 		for (int q : query)
f94ac98860 2016-12-29        kinaba: 			ans.push_back(solve(n, K, epk, dK, q).val);
f94ac98860 2016-12-29        kinaba: 		return ans;
f94ac98860 2016-12-29        kinaba: 	}
f94ac98860 2016-12-29        kinaba: 
f94ac98860 2016-12-29        kinaba: 	// # of solutions in mod K world s.t. x[0] x[1] ... x[n-1] = q
f94ac98860 2016-12-29        kinaba: 	//
f94ac98860 2016-12-29        kinaba: 	// * n <= 50
f94ac98860 2016-12-29        kinaba: 	// * K = BIG
f94ac98860 2016-12-29        kinaba: 	// * must be solved 1000 times in time limits.
f94ac98860 2016-12-29        kinaba: 	mint solve(int n, int K, int epk, const vector<pair<int,int>>& dK, int q)
f94ac98860 2016-12-29        kinaba: 	{
f94ac98860 2016-12-29        kinaba: 		if (n == 1)
f94ac98860 2016-12-29        kinaba: 			return 1;
f94ac98860 2016-12-29        kinaba: 
f94ac98860 2016-12-29        kinaba: 		mint ans = POW(epk, n-1);
f94ac98860 2016-12-29        kinaba: 
f94ac98860 2016-12-29        kinaba: 		for (auto pe : dK) {
f94ac98860 2016-12-29        kinaba: 			int p = pe.first;
f94ac98860 2016-12-29        kinaba: 			int e = pe.second;
f94ac98860 2016-12-29        kinaba: 			int qq = q;
f94ac98860 2016-12-29        kinaba: 			int cnt = 0;
f94ac98860 2016-12-29        kinaba: 			while (qq%p == 0 && cnt<e)
f94ac98860 2016-12-29        kinaba: 				cnt++, qq /= p;
f94ac98860 2016-12-29        kinaba: 			// p^cnt is in gcd(K,q)
f94ac98860 2016-12-29        kinaba: 			if (cnt < e) {
f94ac98860 2016-12-29        kinaba: 				ans *= POW(n, cnt); // div dups...
f94ac98860 2016-12-29        kinaba: 			}
f94ac98860 2016-12-29        kinaba: 			else {
f94ac98860 2016-12-29        kinaba: 				ans *= POW(n, cnt); // or more...
f94ac98860 2016-12-29        kinaba: 			}
f94ac98860 2016-12-29        kinaba: 		}
f94ac98860 2016-12-29        kinaba: 
f94ac98860 2016-12-29        kinaba: 		return ans;
f94ac98860 2016-12-29        kinaba: 	}
f94ac98860 2016-12-29        kinaba: };
f94ac98860 2016-12-29        kinaba: 
f94ac98860 2016-12-29        kinaba: // BEGIN CUT HERE
f94ac98860 2016-12-29        kinaba: #include <ctime>
f94ac98860 2016-12-29        kinaba: double start_time; string timer()
f94ac98860 2016-12-29        kinaba:  { ostringstream os; os << " (" << int((clock()-start_time)/CLOCKS_PER_SEC*1000) << " msec)"; return os.str(); }
f94ac98860 2016-12-29        kinaba: template<typename T> ostream& operator<<(ostream& os, const vector<T>& v)
f94ac98860 2016-12-29        kinaba:  { os << "{ ";
f94ac98860 2016-12-29        kinaba:    for(typename vector<T>::const_iterator it=v.begin(); it!=v.end(); ++it)
f94ac98860 2016-12-29        kinaba:    os << '\"' << *it << '\"' << (it+1==v.end() ? "" : ", "); os << " }"; return os; }
f94ac98860 2016-12-29        kinaba: void verify_case(const vector <int>& Expected, const vector <int>& Received) {
f94ac98860 2016-12-29        kinaba:  bool ok = (Expected == Received);
f94ac98860 2016-12-29        kinaba:  if(ok) cerr << "PASSED" << timer() << endl;  else { cerr << "FAILED" << timer() << endl;
f94ac98860 2016-12-29        kinaba:  cerr << "\to: " << Expected << endl << "\tx: " << Received << endl; } }
f94ac98860 2016-12-29        kinaba: #define CASE(N) {cerr << "Test Case #" << N << "..." << flush; start_time=clock();
f94ac98860 2016-12-29        kinaba: #define END	 verify_case(_, ModEquation().count(n, K, query));}
f94ac98860 2016-12-29        kinaba: int main(){
f94ac98860 2016-12-29        kinaba: 
f94ac98860 2016-12-29        kinaba: CASE(0)
f94ac98860 2016-12-29        kinaba: 	int n = 2;
f94ac98860 2016-12-29        kinaba: 	int K = 2;
f94ac98860 2016-12-29        kinaba: 	int query_[] = {0,1};
f94ac98860 2016-12-29        kinaba: 	  vector <int> query(query_, query_+sizeof(query_)/sizeof(*query_));
f94ac98860 2016-12-29        kinaba: 	int __[] = {3, 1 };
f94ac98860 2016-12-29        kinaba: 	  vector <int> _(__, __+sizeof(__)/sizeof(*__));
f94ac98860 2016-12-29        kinaba: END
f94ac98860 2016-12-29        kinaba: CASE(1)
f94ac98860 2016-12-29        kinaba: 	int n = 2;
f94ac98860 2016-12-29        kinaba: 	int K = 4;
f94ac98860 2016-12-29        kinaba: 	int query_[] = {0,1,2,3};
f94ac98860 2016-12-29        kinaba: 	  vector <int> query(query_, query_+sizeof(query_)/sizeof(*query_));
f94ac98860 2016-12-29        kinaba: 	int __[] = {8, 2, 4, 2 };
f94ac98860 2016-12-29        kinaba: 	  vector <int> _(__, __+sizeof(__)/sizeof(*__));
f94ac98860 2016-12-29        kinaba: END
f94ac98860 2016-12-29        kinaba: CASE(2)
f94ac98860 2016-12-29        kinaba: 	int n = 6;
f94ac98860 2016-12-29        kinaba: 	int K = 6;
f94ac98860 2016-12-29        kinaba: 	int query_[] = {4};
f94ac98860 2016-12-29        kinaba: 	  vector <int> query(query_, query_+sizeof(query_)/sizeof(*query_));
f94ac98860 2016-12-29        kinaba: 	int __[] = {2016 };
f94ac98860 2016-12-29        kinaba: 	  vector <int> _(__, __+sizeof(__)/sizeof(*__));
f94ac98860 2016-12-29        kinaba: END
f94ac98860 2016-12-29        kinaba: CASE(3)
f94ac98860 2016-12-29        kinaba: 	int n = 1;
f94ac98860 2016-12-29        kinaba: 	int K = 2;
f94ac98860 2016-12-29        kinaba: 	int query_[] = {0,0,0,1,1,1};
f94ac98860 2016-12-29        kinaba: 	  vector <int> query(query_, query_+sizeof(query_)/sizeof(*query_));
f94ac98860 2016-12-29        kinaba: 	int __[] = {1, 1, 1, 1, 1, 1 };
f94ac98860 2016-12-29        kinaba: 	  vector <int> _(__, __+sizeof(__)/sizeof(*__));
f94ac98860 2016-12-29        kinaba: END
f94ac98860 2016-12-29        kinaba: /*
f94ac98860 2016-12-29        kinaba: CASE(4)
f94ac98860 2016-12-29        kinaba: 	int n = ;
f94ac98860 2016-12-29        kinaba: 	int K = ;
f94ac98860 2016-12-29        kinaba: 	int query_[] = ;
f94ac98860 2016-12-29        kinaba: 	  vector <int> query(query_, query_+sizeof(query_)/sizeof(*query_));
f94ac98860 2016-12-29        kinaba: 	int __[] = ;
f94ac98860 2016-12-29        kinaba: 	  vector <int> _(__, __+sizeof(__)/sizeof(*__));
f94ac98860 2016-12-29        kinaba: END
f94ac98860 2016-12-29        kinaba: CASE(5)
f94ac98860 2016-12-29        kinaba: 	int n = ;
f94ac98860 2016-12-29        kinaba: 	int K = ;
f94ac98860 2016-12-29        kinaba: 	int query_[] = ;
f94ac98860 2016-12-29        kinaba: 	  vector <int> query(query_, query_+sizeof(query_)/sizeof(*query_));
f94ac98860 2016-12-29        kinaba: 	int __[] = ;
f94ac98860 2016-12-29        kinaba: 	  vector <int> _(__, __+sizeof(__)/sizeof(*__));
f94ac98860 2016-12-29        kinaba: END
f94ac98860 2016-12-29        kinaba: */
f94ac98860 2016-12-29        kinaba: }
f94ac98860 2016-12-29        kinaba: // END CUT HERE