Artifact db64e8ad7fab54e4bc62e950ec4a3dee79a223f3
#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; }
mint& operator/=(mint& x, mint y) { return x *= POW(y, MODVAL - 2); }
mint operator/(mint x, mint y) { return x /= y; }
vector<mint> FAC_(1, 1);
mint FAC(LL n) { while (FAC_.size() <= n) FAC_.push_back(FAC_.back()*LL(FAC_.size())); return FAC_[n]; }
// nCk :: O(log MODVAL) time, O(n) space.
mint C(LL n, LL k) { return k<0 || n<k ? 0 : FAC(n) / (FAC(k) * FAC(n - k)); }
class FibonacciStringSum { public:
int get(int n, int a, int b)
{
mint total = 0;
for (int n0 = 0; n0 <= n; ++n0) {
int n1 = n - n0;
if(n1 <= n0+1)
total += POW(n0, a) * POW(n1, b) * num(n0, n1);
}
return total.val;
}
mint num(int n0, int n1)
{
if (n1 == 0)
return 1;
mint all = 0;
// [10] [0] pat
if (n1 <= n0) {
all += C(n1 + (n0 - n1), n1);
}
// [10] [0] 1 pat
all += C(n1 - 1 + (n0 - n1 + 1), n1 - 1);
return all;
}
};
// 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(_, FibonacciStringSum().get(n, a, b));}
int main(){
CASE(0)
int n = 3;
int a = 0;
int b = 0;
int _ = 5;
END
CASE(1)
int n = 3;
int a = 0;
int b = 1;
int _ = 5;
END
CASE(2)
int n = 10;
int a = 10;
int b = 10;
int _ = 518500021;
END
CASE(3)
int n = 5000;
int a = 20;
int b = 20;
int _ = 880245669;
END
/*
CASE(4)
int n = ;
int a = ;
int b = ;
int _ = ;
END
CASE(5)
int n = ;
int a = ;
int b = ;
int _ = ;
END
*/
}
// END CUT HERE