Artifact 9f6441ed525e874cae729816299274e4b494a8f8
#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; }
class PairsOfStrings { public:
int getNumber(int n, int k)
{
set<int> ds;
for(int d=1; d*d<=n; ++d)
if(n%d == 0) {
ds.insert(d);
ds.insert(n/d);
}
memo.clear();
mint total = 0;
for(int d: ds)
total += count_unit(ds, d, k) * d;
return total.val;
}
map<int, mint> memo;
mint count_unit(const set<int>& ds, int d, int k)
{
if(memo.count(d))
return memo[d];
mint v = POW(k, d);
for(int x: ds) {
if(x>=d)
break;
if(d%x==0)
v -= count_unit(ds, x, k);
}
return memo[d] = v;
}
};
// 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 int& Expected, const 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(_, PairsOfStrings().getNumber(n, k));}
int main(){
CASE(0)
int n = 2;
int k = 2;
int _ = 6;
END
CASE(1)
int n = 3;
int k = 2;
int _ = 20;
END
CASE(2)
int n = 3;
int k = 4;
int _ = 184;
END
CASE(3)
int n = 6;
int k = 2;
int _ = 348;
END
CASE(4)
int n = 100;
int k = 26;
int _ = 46519912;
END
CASE(5)
int n = 100000000;
int k = 26;
int _ = -1;
END
/*
CASE(6)
int n = ;
int k = ;
int _ = ;
END
*/
}
// END CUT HERE