Submission #10058984

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Source Code Expand

#include <iostream>
#include <map>
#include <set>
#include <cmath>
#include <algorithm>
#include <vector>
#include <string>
#include <fstream>
#include <bitset>
#include <queue>
#include <stack>
#include <deque>
#include <complex>
#include <iomanip>
#include <stdio.h>
#include <string.h>
#include <random>
#include <functional>

using std::cin;
using std::cout;
using std::cerr;
using std::endl;

using std::map;
using std::set;
using std::bitset;
using std::vector;
using std::string;
using std::multimap;
using std::multiset;
using std::deque;
using std::queue;
using std::stack;
using std::pair;
using std::iterator;

using std::sort;
using std::stable_sort;
using std::reverse;
using std::max_element;
using std::min_element;
using std::unique;
using std::ios_base;
using std::swap;
using std::fill;

using std::setprecision;
using std::fixed;

typedef long long ll;
typedef pair<int, int> pii;
typedef pair<ll, ll> pll;
typedef vector<int> vi;
typedef vector<long long> vl;
typedef string S;

ll min(ll a, ll b) {return a < b ? a : b;}
ll min(int a, ll b) {return a < b ? a : b;}
ll min(ll a, int b) {return a < b ? a : b;}
ll min(int a, int b) {return a < b ? a : b;}

ll max(ll a, ll b) {return a > b ? a : b;}
ll max(int a, ll b) {return a > b ? a : b;}
ll max(ll a, int b) {return a > b ? a : b;}
ll max(int a, int b) {return a > b ? a : b;}

namespace MySpace{

};

#define F(i, n) for (int (i) = 0; (i) != (n); (i)++)
#define fi first
#define se second
#define re return
#define all(x) (x).begin(), (x).end()

const int MOD = 1e9 + 7;

long long inq(long long a, long long b)
{
    if (b == 0) return 1;
    long long l = inq(a, b / 2);
    if (b % 2) return l * l % MOD * a % MOD;
    return l * l % MOD;
}

int n0, m0;
int fact[5000], ufact[5000];
int dp[310][310][310];
int ways[310][310][310];

long long cnk(long long x, long long k)
{
    return 1LL * fact[x] * ufact[k] % MOD * ufact[x - k] % MOD;
}

signed main()
{
    ios_base::sync_with_stdio(false);
    cin.tie(0);
    cout.tie(0);
    cin >> n0 >> m0;
    fact[0] = 1, ufact[0] = 1;
    for (int i = 1; i <= 300; i++) fact[i] = 1LL * fact[i - 1] * i % MOD, ufact[i] = inq(fact[i], MOD - 2);
    for (int all = 0; all <= n0 + 1; all++)
    {
        ways[0][all][0] = 1;
        for (int i = 0; i < 300; i++)
        {
            for (int j = 0; j <= all; j++)
            {
                ways[i + 1][all][j] = (ways[i + 1][all][j] + 1LL * ways[i][all][j] * j) % MOD;
                ways[i + 1][all][j + 1] = (ways[i + 1][all][j + 1] + 1LL * ways[i][all][j] * (all - j)) % MOD;
            }
        }
    }
    for (int all = 0; all <= n0 + 1; all++)
    {
        for (int x = 0; x <= 300; x++)
        {
            for (int y = 0; y <= all; y++)
            {
                ways[x][all][y] = 1LL * ways[x][all][y] * inq(cnk(all, y), MOD - 2) % MOD;
                ways[x][all][y] = 1LL * ways[x][all][y] * ufact[y] % MOD;
            }
        }
        for (int x = 0; x <= 300; x++)
        {
            for (int y = all - 1; y >= 0; y--) 
                ways[x][all][y] = (ways[x][all][y] + 1LL * ways[x][all][y + 1] * all) % MOD;
        }
    }
    dp[0][1][0] = 1;
    for (int pos = 1; pos <= m0; pos++)
    {
        for (int last = 1; last <= n0; last++)
        {
            for (int pr = 0; pr < pos; pr++)
            {
                for (int wri = 0; wri < last; wri++)
                {
                    for (int blo = 0; blo <= wri; blo++)
                    {
                        dp[pos][last][wri] = (dp[pos][last][wri] + 1LL * dp[pr][wri][blo] * 
                        ways[pos - pr - 1][last - blo][last - wri] % MOD * (wri - blo)) % MOD;
                        if (dp[pr][wri][blo] != 0 && ways[pos - pr - 1][last - blo][last - wri] != 0)
                        {
                            //cout << pos << " " << last << " " << wri << " <- " << pr << " " << wri << " " << blo << endl;
                            //cout << ways[pos - pr - 1][last - blo][last - wri] << endl;
                        }
                    }
                }
            }
        }
    }
    /*cout << endl;
    for (int i = 0; i <= m0; i++)
    {
        for (int j = 0; j <= n0; j++)
        {
            long long s = 0;
            for (int k = 0; k <= j; k++) s = (s + dp[i][j][k]) % MOD;
            cout << s << " ";
        }
        cout << endl;
    }*/
    long long ans = 0;
    for (int pos = 0; pos <= m0; pos++)
    {
        for (int written = n0; written <= n0; written++)
        for (int blocked = 0; blocked <= written; blocked++)
        {
            ans = (ans + 1LL * dp[pos][written][blocked] * ways[m0 - pos][n0 - blocked][n0 - written]) % MOD;
        }
    }
    cout << ans * fact[n0 - 1] % MOD;
}

Submission Info

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