This submission is migrated from previous version of oj.uz, which used different machine for grading. This submission may have different result if resubmitted.
#include <bits/stdc++.h>
#define Loop(x,l,r) for (ll x = (l); x < (r); ++x)
#define LoopR(x,l,r) for (ll x = (r)-1; x >= (l); --x)
typedef long long ll;
typedef std::pair<int, int> pii;
typedef std::pair<ll , ll > pll;
using namespace std;
const int N = 2010;
const int mod = 1e9 + 7;
ll out_of_bound[32];
ll dp[N][N];
int main()
{
cin.tie(0) -> sync_with_stdio(false);
dp[0][0] = 1;
int n, s, t;
cin >> n;
cin >> s >> t;
if (s > t) swap(s, t);
--s; --t;
Loop (i,0,s) Loop (j,0,n) {
dp[i+1][j+1] += dp[i][j];
dp[i+1][j+1] %= mod;
dp[i+1][j-1] += dp[i][j] * j * (j-1);
dp[i+1][j-1] %= mod;
}
Loop (j,0,n) {
dp[s+1][j+1] += dp[s][j];
dp[s+1][j+1] %= mod;
dp[s+1][j] += dp[s][j] * j;
dp[s+1][j] %= mod;
}
Loop (i,s+1,t) Loop (j,1,n) {
dp[i+1][j+1] += dp[i][j];
dp[i+1][j+1] %= mod;
dp[i+1][j-1] += dp[i][j] * (j-1) * (j-1);
dp[i+1][j-1] %= mod;
}
if (t == n-1) {
cout << dp[t][1] << '\n';
return 0;
}
Loop (j,1,n) {
dp[t+1][j+1] += dp[t][j];
dp[t+1][j+1] %= mod;
dp[t+1][j] += dp[t][j] * (j-1);
dp[t+1][j] %= mod;
}
Loop (i,t+1,n-1) Loop (j,2,n) {
dp[i+1][j+1] += dp[i][j];
dp[i+1][j+1] %= mod;
dp[i+1][j-1] += dp[i][j] * ((j-2) * (j-3) + (j-2) + (j-2));
dp[i+1][j-1] %= mod;
}
//Loop (i,0,n) {
// cout << i << ": ";
// Loop (j,0,i+1)
// cout << dp[i][j] << ' ';
// cout << '\n';
//}
cout << dp[n-1][2] << '\n';
}
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