47a150c34b 2015-10-14        kinaba: #include <iostream>
47a150c34b 2015-10-14        kinaba: #include <sstream>
47a150c34b 2015-10-14        kinaba: #include <iomanip>
47a150c34b 2015-10-14        kinaba: #include <vector>
47a150c34b 2015-10-14        kinaba: #include <string>
47a150c34b 2015-10-14        kinaba: #include <map>
47a150c34b 2015-10-14        kinaba: #include <set>
47a150c34b 2015-10-14        kinaba: #include <algorithm>
47a150c34b 2015-10-14        kinaba: #include <numeric>
47a150c34b 2015-10-14        kinaba: #include <iterator>
47a150c34b 2015-10-14        kinaba: #include <functional>
47a150c34b 2015-10-14        kinaba: #include <complex>
47a150c34b 2015-10-14        kinaba: #include <queue>
47a150c34b 2015-10-14        kinaba: #include <stack>
47a150c34b 2015-10-14        kinaba: #include <cmath>
47a150c34b 2015-10-14        kinaba: #include <cassert>
47a150c34b 2015-10-14        kinaba: #include <tuple>
47a150c34b 2015-10-14        kinaba: using namespace std;
47a150c34b 2015-10-14        kinaba: typedef long long LL;
47a150c34b 2015-10-14        kinaba: typedef complex<double> CMP;
47a150c34b 2015-10-14        kinaba: 
47a150c34b 2015-10-14        kinaba: static const unsigned MODVAL = 1000000007;
47a150c34b 2015-10-14        kinaba: struct mint
47a150c34b 2015-10-14        kinaba: {
47a150c34b 2015-10-14        kinaba: 	unsigned val;
47a150c34b 2015-10-14        kinaba: 	mint():val(0){}
47a150c34b 2015-10-14        kinaba: 	mint(int      x):val(x%MODVAL) {}
47a150c34b 2015-10-14        kinaba: 	mint(unsigned x):val(x%MODVAL) {}
47a150c34b 2015-10-14        kinaba: 	mint(LL       x):val(x%MODVAL) {}
47a150c34b 2015-10-14        kinaba: };
47a150c34b 2015-10-14        kinaba: mint& operator+=(mint& x, mint y) { return x = x.val+y.val; }
47a150c34b 2015-10-14        kinaba: mint& operator-=(mint& x, mint y) { return x = x.val-y.val+MODVAL; }
47a150c34b 2015-10-14        kinaba: mint& operator*=(mint& x, mint y) { return x = LL(x.val)*y.val; }
47a150c34b 2015-10-14        kinaba: mint operator+(mint x, mint y) { return x+=y; }
47a150c34b 2015-10-14        kinaba: mint operator-(mint x, mint y) { return x-=y; }
47a150c34b 2015-10-14        kinaba: mint operator*(mint x, mint y) { return x*=y; }
47a150c34b 2015-10-14        kinaba: 
47a150c34b 2015-10-14        kinaba: mint POW(mint x, LL e) { mint v=1; for(;e;x*=x,e>>=1) if(e&1) v*=x; return v; }
47a150c34b 2015-10-14        kinaba: mint& operator/=(mint& x, mint y) { return x *= POW(y, MODVAL-2); }
47a150c34b 2015-10-14        kinaba: mint operator/(mint x, mint y) { return x/=y; }
47a150c34b 2015-10-14        kinaba: 
47a150c34b 2015-10-14        kinaba: vector<mint> FAC_(1,1);
47a150c34b 2015-10-14        kinaba: mint FAC(LL n) { while( FAC_.size()<=n ) FAC_.push_back( FAC_.back()*LL(FAC_.size()) ); return FAC_[size_t(n)]; }
47a150c34b 2015-10-14        kinaba: 
47a150c34b 2015-10-14        kinaba: template<typename T>
47a150c34b 2015-10-14        kinaba: struct DP2
47a150c34b 2015-10-14        kinaba: {
47a150c34b 2015-10-14        kinaba: 	const int N1, N2;
47a150c34b 2015-10-14        kinaba: 	vector<T> data;
47a150c34b 2015-10-14        kinaba: 	DP2(){}
47a150c34b 2015-10-14        kinaba: 	DP2(int N1, int N2, const T& t = T())
47a150c34b 2015-10-14        kinaba: 		: N1(N1), N2(N2), data(N1*N2, t) { assert(data.size()*sizeof(T)<(1<<28)); }
47a150c34b 2015-10-14        kinaba: 	T& operator()(int i1, int i2)
47a150c34b 2015-10-14        kinaba: 		{ return data[ (i1*N2)+i2 ]; }
47a150c34b 2015-10-14        kinaba: 	void swap(DP2& rhs)
47a150c34b 2015-10-14        kinaba: 		{ data.swap(rhs.data); }
47a150c34b 2015-10-14        kinaba: };
47a150c34b 2015-10-14        kinaba: 
47a150c34b 2015-10-14        kinaba: class LineMST { public:
47a150c34b 2015-10-14        kinaba: 
47a150c34b 2015-10-14        kinaba: 	int count(int N, int L)
47a150c34b 2015-10-14        kinaba: 	{
47a150c34b 2015-10-14        kinaba: 		DP2<int> dp(N, L+1, -1);
47a150c34b 2015-10-14        kinaba: 		DP2<int> dp_sub(N, L+1, -1);
47a150c34b 2015-10-14        kinaba: 		return (solve(N-1, L, L, dp, dp_sub)*FAC(N)/2).val;
47a150c34b 2015-10-14        kinaba: 	}
47a150c34b 2015-10-14        kinaba: 
47a150c34b 2015-10-14        kinaba: 	// maximum <= L
47a150c34b 2015-10-14        kinaba: 	mint solve(int N, int L, const int OL, DP2<int>& dp, DP2<int>& dp_sub)
47a150c34b 2015-10-14        kinaba: 	{
47a150c34b 2015-10-14        kinaba: 		if(N==0) return 1;
47a150c34b 2015-10-14        kinaba: 		if(L==0) return 0;
47a150c34b 2015-10-14        kinaba: 		if(dp(N,L) != -1)
47a150c34b 2015-10-14        kinaba: 			return dp(N,L);
47a150c34b 2015-10-14        kinaba: 
47a150c34b 2015-10-14        kinaba: 		mint total = 0;
47a150c34b 2015-10-14        kinaba: 		for(int XL=1; XL<=L; ++XL)
47a150c34b 2015-10-14        kinaba: 			total += solve_sub(N, XL, OL, dp, dp_sub);
47a150c34b 2015-10-14        kinaba: 		return dp(N,L) = total.val;
47a150c34b 2015-10-14        kinaba: 	}
47a150c34b 2015-10-14        kinaba: 
47a150c34b 2015-10-14        kinaba: 	// L = exact maximum.
47a150c34b 2015-10-14        kinaba: 	int solve_sub(int N, int L, const int OL, DP2<int>& dp, DP2<int>& dp_sub) {
47a150c34b 2015-10-14        kinaba: 		if(N==0) return 1;
47a150c34b 2015-10-14        kinaba: 		if(L==0) return 0;
47a150c34b 2015-10-14        kinaba: 		if(dp_sub(N,L) != -1)
47a150c34b 2015-10-14        kinaba: 			return dp_sub(N,L);
47a150c34b 2015-10-14        kinaba: 
47a150c34b 2015-10-14        kinaba: 		mint total = 0;
47a150c34b 2015-10-14        kinaba: 		for(int maxP=1; maxP<=N; ++maxP) {
47a150c34b 2015-10-14        kinaba: 			total +=
47a150c34b 2015-10-14        kinaba: 				mint(solve(maxP-1, L-1, OL, dp, dp_sub))
47a150c34b 2015-10-14        kinaba: 				* solve(N-maxP, L, OL, dp, dp_sub)
47a150c34b 2015-10-14        kinaba: 				* POW(OL-L+1, maxP*(N-maxP+1)-1);
47a150c34b 2015-10-14        kinaba: 		}
47a150c34b 2015-10-14        kinaba: 		return dp_sub(N,L)=total.val;
47a150c34b 2015-10-14        kinaba: 	}
47a150c34b 2015-10-14        kinaba: };
47a150c34b 2015-10-14        kinaba: 
47a150c34b 2015-10-14        kinaba: // BEGIN CUT HERE
47a150c34b 2015-10-14        kinaba: #include <ctime>
47a150c34b 2015-10-14        kinaba: double start_time; string timer()
47a150c34b 2015-10-14        kinaba:  { ostringstream os; os << " (" << int((clock()-start_time)/CLOCKS_PER_SEC*1000) << " msec)"; return os.str(); }
47a150c34b 2015-10-14        kinaba: template<typename T> ostream& operator<<(ostream& os, const vector<T>& v)
47a150c34b 2015-10-14        kinaba:  { os << "{ ";
47a150c34b 2015-10-14        kinaba:    for(typename vector<T>::const_iterator it=v.begin(); it!=v.end(); ++it)
47a150c34b 2015-10-14        kinaba:    os << '\"' << *it << '\"' << (it+1==v.end() ? "" : ", "); os << " }"; return os; }
47a150c34b 2015-10-14        kinaba: void verify_case(const int& Expected, const int& Received) {
47a150c34b 2015-10-14        kinaba:  bool ok = (Expected == Received);
47a150c34b 2015-10-14        kinaba:  if(ok) cerr << "PASSED" << timer() << endl;  else { cerr << "FAILED" << timer() << endl;
47a150c34b 2015-10-14        kinaba:  cerr << "\to: \"" << Expected << '\"' << endl << "\tx: \"" << Received << '\"' << endl; } }
47a150c34b 2015-10-14        kinaba: #define CASE(N) {cerr << "Test Case #" << N << "..." << flush; start_time=clock();
47a150c34b 2015-10-14        kinaba: #define END	 verify_case(_, LineMST().count(N, L));}
47a150c34b 2015-10-14        kinaba: int main(){
47a150c34b 2015-10-14        kinaba: 
47a150c34b 2015-10-14        kinaba: CASE(0)
47a150c34b 2015-10-14        kinaba: 	int N = 3;
47a150c34b 2015-10-14        kinaba: 	int L = 2;
47a150c34b 2015-10-14        kinaba: 	int _ = 15;
47a150c34b 2015-10-14        kinaba: END
47a150c34b 2015-10-14        kinaba: CASE(1)
47a150c34b 2015-10-14        kinaba: 	int N = 2;
47a150c34b 2015-10-14        kinaba: 	int L = 10;
47a150c34b 2015-10-14        kinaba: 	int _ = 10;
47a150c34b 2015-10-14        kinaba: END
47a150c34b 2015-10-14        kinaba: CASE(2)
47a150c34b 2015-10-14        kinaba: 	int N = 3;
47a150c34b 2015-10-14        kinaba: 	int L = 1;
47a150c34b 2015-10-14        kinaba: 	int _ = 3;
47a150c34b 2015-10-14        kinaba: END
47a150c34b 2015-10-14        kinaba: CASE(3)
47a150c34b 2015-10-14        kinaba: 	int N = 8;
47a150c34b 2015-10-14        kinaba: 	int L = 41;
47a150c34b 2015-10-14        kinaba: 	int _ = 655468587;
47a150c34b 2015-10-14        kinaba: END
47a150c34b 2015-10-14        kinaba: CASE(4)
47a150c34b 2015-10-14        kinaba: 	int N = 50;
47a150c34b 2015-10-14        kinaba: 	int L = 50;
47a150c34b 2015-10-14        kinaba: 	int _ = 699887037;
47a150c34b 2015-10-14        kinaba: END
47a150c34b 2015-10-14        kinaba: CASE(4)
47a150c34b 2015-10-14        kinaba: 	int N = 200;
47a150c34b 2015-10-14        kinaba: 	int L = 200;
47a150c34b 2015-10-14        kinaba: 	int _ = 152699064;
47a150c34b 2015-10-14        kinaba: END
47a150c34b 2015-10-14        kinaba: /*
47a150c34b 2015-10-14        kinaba: CASE(5)
47a150c34b 2015-10-14        kinaba: 	int N = ;
47a150c34b 2015-10-14        kinaba: 	int L = ;
47a150c34b 2015-10-14        kinaba: 	int _ = ;
47a150c34b 2015-10-14        kinaba: END
47a150c34b 2015-10-14        kinaba: CASE(6)
47a150c34b 2015-10-14        kinaba: 	int N = ;
47a150c34b 2015-10-14        kinaba: 	int L = ;
47a150c34b 2015-10-14        kinaba: 	int _ = ;
47a150c34b 2015-10-14        kinaba: END
47a150c34b 2015-10-14        kinaba: */
47a150c34b 2015-10-14        kinaba: }
47a150c34b 2015-10-14        kinaba: // END CUT HERE