Artifact 527ef29abc31b65231b9849c635227471eb24494
#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; }
vector< vector<mint> > CP_;
mint C(int n, int 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 SumOverPermutations { public:
int N;
vector<int> memoOO, memoCO, memoCC;
int findSum(int n)
{
N = n;
memoOO.assign(N+1, -1);
memoCO.assign(N+1, -1);
memoCC.assign(N+1, -1);
return recOO(n);
}
int recOO(int k) {
if(k == 0) return 1;
if(k == 1) return N;
if(memoOO[k] != -1) return memoOO[k];
mint total = 0;
total += mint(N) * recCO(k-1); // left
total += mint(N) * recCO(k-1); // right
for(int i=1; i+1<k; ++i) // mid
total += mint(N) * recCO(i) * recCO(k-1-i) * C(k-1, i);
return memoOO[k] = total.val;
}
int recCO(int k) {
if(k == 0) return 1;
if(k == 1) return N-1;
if(memoCO[k] != -1) return memoCO[k];
mint total = 0;
total += mint(N-1) * recCO(k-1); // left
total += mint(N) * recCC(k-1); // right
for(int i=1; i+1<k; ++i) // mid
total += mint(N) * recCC(i) * recCO(k-1-i) * C(k-1, i);
return memoCO[k] = total.val;
}
mint recCC(int k) {
if(k == 0) return 1;
if(k == 1) return N-2;
if(memoCC[k] != -1) return memoCC[k];
mint total = 0;
total += mint(N-1) * recCC(k-1); // left
total += mint(N-1) * recCC(k-1); // right
for(int i=1; i+1<k; ++i) // mid
total += mint(N) * recCC(i) * recCC(k-1-i) * C(k-1, i);
return memoCC[k] = total.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(_, SumOverPermutations().findSum(n));}
int main(){
CASE(0)
int n = 2;
int _ = 4;
END
CASE(1)
int n = 3;
int _ = 66;
END
CASE(2)
int n = 10;
int _ = 58310114;
END
CASE(3)
int n = 3900;
int _ = 940560814;
END
/*
CASE(4)
int n = ;
int _ = ;
END
CASE(5)
int n = ;
int _ = ;
END
*/
}
// END CUT HERE