Artifact 7fa2189be95e994e72cf7090925ac133b9f5ed22
#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>
using namespace std;
typedef long long LL;
typedef long double LD;
typedef complex<LD> CMP;
static const int MODVAL = 1000000007;
struct mint
{
int val;
mint():val(0){}
mint(int x):val(x%MODVAL) {}
mint(size_t 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; }
vector< vector<mint> > CP_;
mint C(LL n, LL k) {
while( CP_.size() <= n ) {
int nn = CP_.size();
CP_.push_back(vector<mint>(nn+1,1));
for(int kk=1; kk<nn; ++kk)
CP_[nn][kk] = CP_[nn-1][kk-1] + CP_[nn-1][kk];
}
return k<0 || n<k ? 0 : CP_[n][k];
}
class KingdomAndCities { public:
int howMany(int N, int M, int K)
{
if( M == 0 ) return zero(N, K).val;
if( M == 1 ) return one(N, K).val;
return two(N, K).val;
}
mint zero_may_be_disconnected(int N, int K)
{
return C(N*(N-1)/2, K);
}
map<pair<int,int>, mint> memo;
mint zero(int N, int K)
{
pair<int,int> key(N, K);
if(memo.count(key))
return memo[key];
mint sum = zero_may_be_disconnected(N, K);
for(int NA=1; NA<=N-1; ++NA)
for(int KA=0; KA<=K; ++KA)
sum -= C(N-1,NA-1)*zero(NA,KA)*zero_may_be_disconnected(N-NA, K-KA);
return memo[key] = sum;
}
mint one(int N, int K)
{
mint sum = zero(N-1,K-2)*C(N-1,2);
for(int NA=1; NA<=N-2; ++NA)
for(int KA=0; KA<=K-2; ++KA)
sum += C(N-2,NA-1)*zero(NA,KA)*NA*(N-1-NA)*zero(N-1-NA,K-2-KA);
return sum;
}
mint two(int N, int K)
{
mint sum = one(N-1,K-2)*C(N-2,2);
for(int NA=1; NA<=N-2; ++NA)
for(int KA=0; KA<=K-2; ++KA)
sum += C(N-2,NA-1)*one(NA,KA)*(NA-1)*(N-1-NA)*zero(N-1-NA,K-2-KA);
--N, --K;
sum += zero(N-1,K-2)*(N-1)*(N-1);
for(int NA=1; NA<=N-2; ++NA)
for(int KA=0; KA<=K-2; ++KA)
sum += C(N-1,NA)*zero(NA,KA)*NA*(N-1-NA)*zero(N-1-NA,K-2-KA);
return sum;
}
};
// 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(_, KingdomAndCities().howMany(N, M, K));}
int main(){
CASE(0)
int N = 3;
int M = 0;
int K = 3;
int _ = 1;
END
CASE(1)
int N = 4;
int M = 1;
int K = 4;
int _ = 9;
END
CASE(2)
int N = 5;
int M = 2;
int K = 11;
int _ = 0;
END
CASE(3)
int N = 5;
int M = 0;
int K = 8;
int _ = 45;
END
CASE(4)
int N = 10;
int M = 2;
int K = 20;
int _ = 150810825;
END
CASE(5)
int N = 3;
int M = 2;
int K = 3;
int _ = 1;
END
/*
CASE(6)
int N = ;
int M = ;
int K = ;
int _ = ;
END
*/
}
// END CUT HERE