ed7454da2a 2016-10-26        kinaba: #include <iostream>
ed7454da2a 2016-10-26        kinaba: #include <sstream>
ed7454da2a 2016-10-26        kinaba: #include <iomanip>
ed7454da2a 2016-10-26        kinaba: #include <vector>
ed7454da2a 2016-10-26        kinaba: #include <string>
ed7454da2a 2016-10-26        kinaba: #include <map>
ed7454da2a 2016-10-26        kinaba: #include <set>
ed7454da2a 2016-10-26        kinaba: #include <algorithm>
ed7454da2a 2016-10-26        kinaba: #include <numeric>
ed7454da2a 2016-10-26        kinaba: #include <iterator>
ed7454da2a 2016-10-26        kinaba: #include <functional>
ed7454da2a 2016-10-26        kinaba: #include <complex>
ed7454da2a 2016-10-26        kinaba: #include <queue>
ed7454da2a 2016-10-26        kinaba: #include <stack>
ed7454da2a 2016-10-26        kinaba: #include <cmath>
ed7454da2a 2016-10-26        kinaba: #include <cassert>
ed7454da2a 2016-10-26        kinaba: #include <tuple>
ed7454da2a 2016-10-26        kinaba: using namespace std;
ed7454da2a 2016-10-26        kinaba: typedef long long LL;
ed7454da2a 2016-10-26        kinaba: typedef complex<double> CMP;
ed7454da2a 2016-10-26        kinaba: 
ed7454da2a 2016-10-26        kinaba: static const unsigned MODVAL = 1000000007;
ed7454da2a 2016-10-26        kinaba: struct mint
ed7454da2a 2016-10-26        kinaba: {
ed7454da2a 2016-10-26        kinaba: 	unsigned val;
ed7454da2a 2016-10-26        kinaba: 	mint() :val(0) {}
ed7454da2a 2016-10-26        kinaba: 	mint(int      x) :val(x%MODVAL) {}
ed7454da2a 2016-10-26        kinaba: 	mint(unsigned x) :val(x%MODVAL) {}
ed7454da2a 2016-10-26        kinaba: 	mint(LL       x) :val(x%MODVAL) {}
ed7454da2a 2016-10-26        kinaba: };
ed7454da2a 2016-10-26        kinaba: mint& operator+=(mint& x, mint y) { return x = x.val + y.val; }
ed7454da2a 2016-10-26        kinaba: mint& operator-=(mint& x, mint y) { return x = x.val - y.val + MODVAL; }
ed7454da2a 2016-10-26        kinaba: mint& operator*=(mint& x, mint y) { return x = LL(x.val)*y.val; }
ed7454da2a 2016-10-26        kinaba: mint operator+(mint x, mint y) { return x += y; }
ed7454da2a 2016-10-26        kinaba: mint operator-(mint x, mint y) { return x -= y; }
ed7454da2a 2016-10-26        kinaba: mint operator*(mint x, mint y) { return x *= y; }
ed7454da2a 2016-10-26        kinaba: 
ed7454da2a 2016-10-26        kinaba: mint POW(mint x, LL e) { mint v = 1; for (; e; x *= x, e >>= 1) if (e & 1) v *= x; return v; }
ed7454da2a 2016-10-26        kinaba: mint& operator/=(mint& x, mint y) { return x *= POW(y, MODVAL - 2); }
ed7454da2a 2016-10-26        kinaba: mint operator/(mint x, mint y) { return x /= y; }
ed7454da2a 2016-10-26        kinaba: 
ed7454da2a 2016-10-26        kinaba: vector<mint> FAC_(1, 1);
ed7454da2a 2016-10-26        kinaba: mint FAC(LL n) { while (FAC_.size() <= n) FAC_.push_back(FAC_.back()*LL(FAC_.size())); return FAC_[n]; }
ed7454da2a 2016-10-26        kinaba: 
ed7454da2a 2016-10-26        kinaba: // nCk :: O(log MODVAL) time, O(n) space.
ed7454da2a 2016-10-26        kinaba: mint C(LL n, LL k) { return k<0 || n<k ? 0 : FAC(n) / (FAC(k) * FAC(n - k)); }
ed7454da2a 2016-10-26        kinaba: 
ed7454da2a 2016-10-26        kinaba: class FibonacciStringSum { public:
ed7454da2a 2016-10-26        kinaba: 	int get(int n, int a, int b)
ed7454da2a 2016-10-26        kinaba: 	{
ed7454da2a 2016-10-26        kinaba: 		mint total = 0;
ed7454da2a 2016-10-26        kinaba: 		for (int n0 = 0; n0 <= n; ++n0) {
ed7454da2a 2016-10-26        kinaba: 			int n1 = n - n0;
ed7454da2a 2016-10-26        kinaba: 			if(n1 <= n0+1)
ed7454da2a 2016-10-26        kinaba: 				total += POW(n0, a) * POW(n1, b) * num(n0, n1);
ed7454da2a 2016-10-26        kinaba: 		}
ed7454da2a 2016-10-26        kinaba: 		return total.val;
ed7454da2a 2016-10-26        kinaba: 	}
ed7454da2a 2016-10-26        kinaba: 
ed7454da2a 2016-10-26        kinaba: 	mint num(int n0, int n1)
ed7454da2a 2016-10-26        kinaba: 	{
ed7454da2a 2016-10-26        kinaba: 		if (n1 == 0)
ed7454da2a 2016-10-26        kinaba: 			return 1;
ed7454da2a 2016-10-26        kinaba: 
ed7454da2a 2016-10-26        kinaba: 		mint all = 0;
ed7454da2a 2016-10-26        kinaba: 		// [10] [0] pat
ed7454da2a 2016-10-26        kinaba: 		if (n1 <= n0) {
ed7454da2a 2016-10-26        kinaba: 			all += C(n1 + (n0 - n1), n1);
ed7454da2a 2016-10-26        kinaba: 		}
ed7454da2a 2016-10-26        kinaba: 		// [10] [0] 1 pat
ed7454da2a 2016-10-26        kinaba: 		all += C(n1 - 1 + (n0 - n1 + 1), n1 - 1);
ed7454da2a 2016-10-26        kinaba: 		return all;
ed7454da2a 2016-10-26        kinaba: 	}
ed7454da2a 2016-10-26        kinaba: };
ed7454da2a 2016-10-26        kinaba: 
ed7454da2a 2016-10-26        kinaba: // BEGIN CUT HERE
ed7454da2a 2016-10-26        kinaba: #include <ctime>
ed7454da2a 2016-10-26        kinaba: double start_time; string timer()
ed7454da2a 2016-10-26        kinaba:  { ostringstream os; os << " (" << int((clock()-start_time)/CLOCKS_PER_SEC*1000) << " msec)"; return os.str(); }
ed7454da2a 2016-10-26        kinaba: template<typename T> ostream& operator<<(ostream& os, const vector<T>& v)
ed7454da2a 2016-10-26        kinaba:  { os << "{ ";
ed7454da2a 2016-10-26        kinaba:    for(typename vector<T>::const_iterator it=v.begin(); it!=v.end(); ++it)
ed7454da2a 2016-10-26        kinaba:    os << '\"' << *it << '\"' << (it+1==v.end() ? "" : ", "); os << " }"; return os; }
ed7454da2a 2016-10-26        kinaba: void verify_case(const int& Expected, const int& Received) {
ed7454da2a 2016-10-26        kinaba:  bool ok = (Expected == Received);
ed7454da2a 2016-10-26        kinaba:  if(ok) cerr << "PASSED" << timer() << endl;  else { cerr << "FAILED" << timer() << endl;
ed7454da2a 2016-10-26        kinaba:  cerr << "\to: \"" << Expected << '\"' << endl << "\tx: \"" << Received << '\"' << endl; } }
ed7454da2a 2016-10-26        kinaba: #define CASE(N) {cerr << "Test Case #" << N << "..." << flush; start_time=clock();
ed7454da2a 2016-10-26        kinaba: #define END	 verify_case(_, FibonacciStringSum().get(n, a, b));}
ed7454da2a 2016-10-26        kinaba: int main(){
ed7454da2a 2016-10-26        kinaba: 
ed7454da2a 2016-10-26        kinaba: CASE(0)
ed7454da2a 2016-10-26        kinaba: 	int n = 3;
ed7454da2a 2016-10-26        kinaba: 	int a = 0;
ed7454da2a 2016-10-26        kinaba: 	int b = 0;
ed7454da2a 2016-10-26        kinaba: 	int _ = 5;
ed7454da2a 2016-10-26        kinaba: END
ed7454da2a 2016-10-26        kinaba: CASE(1)
ed7454da2a 2016-10-26        kinaba: 	int n = 3;
ed7454da2a 2016-10-26        kinaba: 	int a = 0;
ed7454da2a 2016-10-26        kinaba: 	int b = 1;
ed7454da2a 2016-10-26        kinaba: 	int _ = 5;
ed7454da2a 2016-10-26        kinaba: END
ed7454da2a 2016-10-26        kinaba: CASE(2)
ed7454da2a 2016-10-26        kinaba: 	int n = 10;
ed7454da2a 2016-10-26        kinaba: 	int a = 10;
ed7454da2a 2016-10-26        kinaba: 	int b = 10;
ed7454da2a 2016-10-26        kinaba: 	int _ = 518500021;
ed7454da2a 2016-10-26        kinaba: END
ed7454da2a 2016-10-26        kinaba: CASE(3)
ed7454da2a 2016-10-26        kinaba: 	int n = 5000;
ed7454da2a 2016-10-26        kinaba: 	int a = 20;
ed7454da2a 2016-10-26        kinaba: 	int b = 20;
ed7454da2a 2016-10-26        kinaba: 	int _ = 880245669;
ed7454da2a 2016-10-26        kinaba: END
ed7454da2a 2016-10-26        kinaba: /*
ed7454da2a 2016-10-26        kinaba: CASE(4)
ed7454da2a 2016-10-26        kinaba: 	int n = ;
ed7454da2a 2016-10-26        kinaba: 	int a = ;
ed7454da2a 2016-10-26        kinaba: 	int b = ;
ed7454da2a 2016-10-26        kinaba: 	int _ = ;
ed7454da2a 2016-10-26        kinaba: END
ed7454da2a 2016-10-26        kinaba: CASE(5)
ed7454da2a 2016-10-26        kinaba: 	int n = ;
ed7454da2a 2016-10-26        kinaba: 	int a = ;
ed7454da2a 2016-10-26        kinaba: 	int b = ;
ed7454da2a 2016-10-26        kinaba: 	int _ = ;
ed7454da2a 2016-10-26        kinaba: END
ed7454da2a 2016-10-26        kinaba: */
ed7454da2a 2016-10-26        kinaba: }
ed7454da2a 2016-10-26        kinaba: // END CUT HERE