## https://yukicoder.me/problems/no/2975 class CombinationCalculator: """ modを考慮したPermutation, Combinationを計算するためのクラス """ def __init__(self, size, mod): self.mod = mod self.factorial = [0] * (size + 1) self.factorial[0] = 1 for i in range(1, size + 1): self.factorial[i] = (i * self.factorial[i - 1]) % self.mod self.inv_factorial = [0] * (size + 1) self.inv_factorial[size] = pow(self.factorial[size], self.mod - 2, self.mod) for i in reversed(range(size)): self.inv_factorial[i] = ((i + 1) * self.inv_factorial[i + 1]) % self.mod def calc_combination(self, n, r): if n < 0 or n < r or r < 0: return 0 if r == 0 or n == r: return 1 ans = self.inv_factorial[n - r] * self.inv_factorial[r] ans %= self.mod ans *= self.factorial[n] ans %= self.mod return ans def calc_permutation(self, n, r): if n < 0 or n < r: return 0 ans = self.inv_factorial[n - r] ans *= self.factorial[n] ans %= self.mod return ans def main(): N, M, P = map(int, input().split()) combi = CombinationCalculator(N, P) dp = [1] for m in range(1, N + 1): new_dp = [0] * (min(M, m) + 1) for n in range(len(dp)): new_dp[n] += dp[n] new_dp[n] %= P if n + 1 < len(new_dp): new_dp[n + 1] += (m * dp[n]) % P new_dp[n + 1] %= P dp = new_dp answer = 0 for m in range(1, M + 1): ans = (combi.calc_combination(M, m) * dp[m]) % P ans *= combi.factorial[M - m] ans %= P answer += ans answer %= P y = pow(combi.calc_permutation(N, M), P - 2, P) answer *= y answer %= P print(answer) if __name__ == "__main__": main()