Kortit II

#include <vector>
#include <iostream>
#include <cmath>
#include <tuple>
using namespace std;

const int MOD = 1000000007;

vector<vector<long long>> triangle() {
	vector<vector<long long>> tri(2001, vector<long long>(2001, 0));
	tri[1][1] = 0;
	tri[2][1] = 1;
	for (int n = 2; n < 2000; ++n) {
		for (int x = 1; x <= n; ++x) {
			tri[n + 1][x] = (x * tri[n][x] + (n + 1 - x) * tri[n][x - 1] + n * tri[n - 1][x - 1]) % MOD;
		}
	}
	return tri;
}

const vector<vector<long long>> tri = triangle();

vector<vector<long long>> coeffs(int n) {
	vector<vector<long long>> C(n + 1, vector<long long>(n + 1, 0));
	for (int i = 0; i <= n; i++) {
		C[i][0] = 1;
		C[i][i] = 1;
	}

	for (int i = 1; i <= n; i++) {
		for (int j = 1; j < i; j++) {
			C[i][j] = C[i - 1][j - 1] + C[i - 1][j] % MOD;
		}
	}

	return C;
}

const vector<vector<long long>> c = coeffs(2001);

long long mpow(long long base, long long exp, long long mod) {
	long long result = 1;
	base = base % mod;
	while (exp > 0) {
		if (exp % 2 == 1) {
			result = (result * base) % mod;
		}
		exp = exp >> 1;
		base = (base * base) % mod;
	}
	return result;
}


long long fact(int n) {
	long long result = 1;
	for (int i = 1; i <= n; ++i) {
		result = (result * i) % MOD;
	}
	return result;
}

long long perm(int n, int x) {
	long long result = 1;
	for (int i = 0; i < x; ++i) {
		result = (result * (n - i)) % MOD;
	}
	return result;
}

long long solve(int n, int a, int b) {
	int req = (a + b);
	if (req > n || req == 1 || a == n || b == n) {
		return 0;
	}
	if (a == 0 && b == 0) {
		return fact(n);
	}
	int x = n - req;
	long long result = (tri[req][a] * fact(req) % MOD * fact(x) % MOD * mpow(c[n][x], 2, MOD)) % MOD;
	return result;
}

int main() {
	int t;
	cin >> t;
	vector<tuple<int, int, int>> inputs;
	for (int i = 0; i < t; ++i) {
		int n, a, b;
		cin >> n >> a >> b;
		inputs.push_back(make_tuple(n, a, b));
	}
	for (tuple<int, int, int> input : inputs) {
		int n, a, b;
		n = get<0>(input);
		a = get<1>(input);
		b = get<2>(input);
		int result = solve(n, a, b);
		cout << result << endl;
	}
	return 0;
}

Test 1

Group: 1, 2, 3, 4, 5

Verdict: ACCEPTED

Test 2

Group: 2, 3, 4, 5

Verdict: ACCEPTED

Test 3

Group: 3, 4, 5

Verdict: ACCEPTED

Test 4

Group: 4, 5

Verdict: ACCEPTED

Test 5

Group: 5

Verdict: ACCEPTED

Test 6

Group: 5

Verdict: ACCEPTED