c9a076d509 2014-01-11        kinaba: #include <iostream>
c9a076d509 2014-01-11        kinaba: #include <sstream>
c9a076d509 2014-01-11        kinaba: #include <iomanip>
c9a076d509 2014-01-11        kinaba: #include <vector>
c9a076d509 2014-01-11        kinaba: #include <string>
c9a076d509 2014-01-11        kinaba: #include <map>
c9a076d509 2014-01-11        kinaba: #include <set>
c9a076d509 2014-01-11        kinaba: #include <algorithm>
c9a076d509 2014-01-11        kinaba: #include <numeric>
c9a076d509 2014-01-11        kinaba: #include <iterator>
c9a076d509 2014-01-11        kinaba: #include <functional>
c9a076d509 2014-01-11        kinaba: #include <complex>
c9a076d509 2014-01-11        kinaba: #include <queue>
c9a076d509 2014-01-11        kinaba: #include <stack>
c9a076d509 2014-01-11        kinaba: #include <cmath>
c9a076d509 2014-01-11        kinaba: #include <cassert>
c9a076d509 2014-01-11        kinaba: #include <tuple>
c9a076d509 2014-01-11        kinaba: using namespace std;
c9a076d509 2014-01-11        kinaba: typedef long long LL;
c9a076d509 2014-01-11        kinaba: typedef complex<double> CMP;
c9a076d509 2014-01-11        kinaba: 
c9a076d509 2014-01-11        kinaba: static const unsigned MODVAL = 1000000007;
c9a076d509 2014-01-11        kinaba: struct mint
c9a076d509 2014-01-11        kinaba: {
c9a076d509 2014-01-11        kinaba: 	unsigned val;
c9a076d509 2014-01-11        kinaba: 	mint():val(0){}
c9a076d509 2014-01-11        kinaba: 	mint(int      x):val(x%MODVAL) {}
c9a076d509 2014-01-11        kinaba: 	mint(unsigned x):val(x%MODVAL) {}
c9a076d509 2014-01-11        kinaba: 	mint(LL       x):val(x%MODVAL) {}
c9a076d509 2014-01-11        kinaba: };
c9a076d509 2014-01-11        kinaba: mint& operator+=(mint& x, mint y) { return x = x.val+y.val; }
c9a076d509 2014-01-11        kinaba: mint& operator-=(mint& x, mint y) { return x = x.val-y.val+MODVAL; }
c9a076d509 2014-01-11        kinaba: mint& operator*=(mint& x, mint y) { return x = LL(x.val)*y.val; }
c9a076d509 2014-01-11        kinaba: mint operator+(mint x, mint y) { return x+=y; }
c9a076d509 2014-01-11        kinaba: mint operator-(mint x, mint y) { return x-=y; }
c9a076d509 2014-01-11        kinaba: mint operator*(mint x, mint y) { return x*=y; }
c9a076d509 2014-01-11        kinaba: 
c9a076d509 2014-01-11        kinaba: mint POW(mint x, LL e) { mint v=1; for(;e;x*=x,e>>=1) if(e&1) v*=x; return v; }
c9a076d509 2014-01-11        kinaba: 
c9a076d509 2014-01-11        kinaba: class PairsOfStrings { public:
c9a076d509 2014-01-11        kinaba: 	int getNumber(int n, int k)
c9a076d509 2014-01-11        kinaba: 	{
c9a076d509 2014-01-11        kinaba: 		set<int> ds;
c9a076d509 2014-01-11        kinaba: 		for(int d=1; d*d<=n; ++d)
c9a076d509 2014-01-11        kinaba: 			if(n%d == 0) {
c9a076d509 2014-01-11        kinaba: 				ds.insert(d);
c9a076d509 2014-01-11        kinaba: 				ds.insert(n/d);
c9a076d509 2014-01-11        kinaba: 			}
c9a076d509 2014-01-11        kinaba: 
c9a076d509 2014-01-11        kinaba: 		memo.clear();
c9a076d509 2014-01-11        kinaba: 
c9a076d509 2014-01-11        kinaba: 		mint total = 0;
c9a076d509 2014-01-11        kinaba: 		for(int d: ds)
c9a076d509 2014-01-11        kinaba: 			total += count_unit(ds, d, k) * d;
c9a076d509 2014-01-11        kinaba: 		return total.val;
c9a076d509 2014-01-11        kinaba: 	}
c9a076d509 2014-01-11        kinaba: 
c9a076d509 2014-01-11        kinaba: 	map<int, mint> memo;
c9a076d509 2014-01-11        kinaba: 	mint count_unit(const set<int>& ds, int d, int k)
c9a076d509 2014-01-11        kinaba: 	{
c9a076d509 2014-01-11        kinaba: 		if(memo.count(d))
c9a076d509 2014-01-11        kinaba: 			return memo[d];
c9a076d509 2014-01-11        kinaba: 
c9a076d509 2014-01-11        kinaba: 		mint v = POW(k, d);
c9a076d509 2014-01-11        kinaba: 		for(int x: ds) {
c9a076d509 2014-01-11        kinaba: 			if(x>=d)
c9a076d509 2014-01-11        kinaba: 				break;
c9a076d509 2014-01-11        kinaba: 			if(d%x==0)
c9a076d509 2014-01-11        kinaba: 				v -= count_unit(ds, x, k);
c9a076d509 2014-01-11        kinaba: 		}
c9a076d509 2014-01-11        kinaba: 		return memo[d] = v;
c9a076d509 2014-01-11        kinaba: 	}
c9a076d509 2014-01-11        kinaba: };
c9a076d509 2014-01-11        kinaba: 
c9a076d509 2014-01-11        kinaba: // BEGIN CUT HERE
c9a076d509 2014-01-11        kinaba: #include <ctime>
c9a076d509 2014-01-11        kinaba: double start_time; string timer()
c9a076d509 2014-01-11        kinaba:  { ostringstream os; os << " (" << int((clock()-start_time)/CLOCKS_PER_SEC*1000) << " msec)"; return os.str(); }
c9a076d509 2014-01-11        kinaba: template<typename T> ostream& operator<<(ostream& os, const vector<T>& v)
c9a076d509 2014-01-11        kinaba:  { os << "{ ";
c9a076d509 2014-01-11        kinaba:    for(typename vector<T>::const_iterator it=v.begin(); it!=v.end(); ++it)
c9a076d509 2014-01-11        kinaba:    os << '\"' << *it << '\"' << (it+1==v.end() ? "" : ", "); os << " }"; return os; }
c9a076d509 2014-01-11        kinaba: void verify_case(const int& Expected, const int& Received) {
c9a076d509 2014-01-11        kinaba:  bool ok = (Expected == Received);
c9a076d509 2014-01-11        kinaba:  if(ok) cerr << "PASSED" << timer() << endl;  else { cerr << "FAILED" << timer() << endl;
c9a076d509 2014-01-11        kinaba:  cerr << "\to: \"" << Expected << '\"' << endl << "\tx: \"" << Received << '\"' << endl; } }
c9a076d509 2014-01-11        kinaba: #define CASE(N) {cerr << "Test Case #" << N << "..." << flush; start_time=clock();
c9a076d509 2014-01-11        kinaba: #define END	 verify_case(_, PairsOfStrings().getNumber(n, k));}
c9a076d509 2014-01-11        kinaba: int main(){
c9a076d509 2014-01-11        kinaba: 
c9a076d509 2014-01-11        kinaba: CASE(0)
c9a076d509 2014-01-11        kinaba: 	int n = 2;
c9a076d509 2014-01-11        kinaba: 	int k = 2;
c9a076d509 2014-01-11        kinaba: 	int _ = 6;
c9a076d509 2014-01-11        kinaba: END
c9a076d509 2014-01-11        kinaba: CASE(1)
c9a076d509 2014-01-11        kinaba: 	int n = 3;
c9a076d509 2014-01-11        kinaba: 	int k = 2;
c9a076d509 2014-01-11        kinaba: 	int _ = 20;
c9a076d509 2014-01-11        kinaba: END
c9a076d509 2014-01-11        kinaba: CASE(2)
c9a076d509 2014-01-11        kinaba: 	int n = 3;
c9a076d509 2014-01-11        kinaba: 	int k = 4;
c9a076d509 2014-01-11        kinaba: 	int _ = 184;
c9a076d509 2014-01-11        kinaba: END
c9a076d509 2014-01-11        kinaba: CASE(3)
c9a076d509 2014-01-11        kinaba: 	int n = 6;
c9a076d509 2014-01-11        kinaba: 	int k = 2;
c9a076d509 2014-01-11        kinaba: 	int _ = 348;
c9a076d509 2014-01-11        kinaba: END
c9a076d509 2014-01-11        kinaba: CASE(4)
c9a076d509 2014-01-11        kinaba: 	int n = 100;
c9a076d509 2014-01-11        kinaba: 	int k = 26;
c9a076d509 2014-01-11        kinaba: 	int _ = 46519912;
c9a076d509 2014-01-11        kinaba: END
c9a076d509 2014-01-11        kinaba: CASE(5)
c9a076d509 2014-01-11        kinaba: 	int n = 100000000;
c9a076d509 2014-01-11        kinaba: 	int k = 26;
c9a076d509 2014-01-11        kinaba: 	int _ = -1;
c9a076d509 2014-01-11        kinaba: END
c9a076d509 2014-01-11        kinaba: /*
c9a076d509 2014-01-11        kinaba: CASE(6)
c9a076d509 2014-01-11        kinaba: 	int n = ;
c9a076d509 2014-01-11        kinaba: 	int k = ;
c9a076d509 2014-01-11        kinaba: 	int _ = ;
c9a076d509 2014-01-11        kinaba: END
c9a076d509 2014-01-11        kinaba: */
c9a076d509 2014-01-11        kinaba: }
c9a076d509 2014-01-11        kinaba: // END CUT HERE