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Artifact 86bec40a9221e580f7322c86d2996ef4d15640e7


#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;

int K;

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; }

vector<mint> solve(int N, vector<mint> q)
{
	if(N == 1)
		return vector<mint>(1, mint(1));

	vector<mint> p(N);
	for(int s=0; s<N; ++s) {
		int d = ((N+1-K)%N+N)%N;
		if(s == d) {
			p[s] = 2 * (d<N-1 ? q[d]/2 : mint(0));
			break;
		}
	}
	for(int s=0; s<N; ++s) {
		int d = ((N+1-K)%N+N)%N;
		if(s != d) {
			p[s] = p[d]/2 + (d<N-1 ? q[d]/2 : mint(0));
		}
	}
	return p;
}

class BearCircleGame { public:
	int winProbability(int n, int k)
	{
		K = k;
		vector<mint> p;
		for(int nn=1; nn<=n; ++nn)
			p = solve(nn, p);
		return p[0].val;
	}
};

// 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(_, BearCircleGame().winProbability(n, k));}
int main(){

CASE(0)
	int n = 2; 
	int k = 1; 
	int _ = 333333336; 
END
CASE(1)
	int n = 2; 
	int k = 2; 
	int _ = 1; 
END
CASE(2)
	int n = 3; 
	int k = 2; 
	int _ = 142857144; 
END
CASE(3)
	int n = 3; 
	int k = 1; 
	int _ = 238095240; 
END
CASE(4)
	int n = 4; 
	int k = 4; 
	int _ = 142857144; 
END
CASE(5)
	int n = 5; 
	int k = 1000000000; 
	int _ = 142857144; 
END
CASE(6)
	int n = 2000; 
	int k = 123; 
	int _ = 429232785; 
END
CASE(7)
	int n = 1987; 
	int k = 987654321; 
	int _ = 623410299; 
END
/*
CASE(8)
	int n = ; 
	int k = ; 
	int _ = ; 
END
CASE(9)
	int n = ; 
	int k = ; 
	int _ = ; 
END
*/
}
// END CUT HERE