class Combination: """ SIZEが10**6程度以下の二項係数を何回も呼び出したいときに使う 使い方: comb = Combination(SIZE, MOD) comb(10, 3) => 120 """ def __init__(self, N, MOD=10 ** 9 + 7): self.MOD = MOD self.__make_factorial_list(N) def __call__(self, n, k): if k < 0 or k > n: return 0 res = self.fact[n] * self.inv[k] % self.MOD res = res * self.inv[n - k] % self.MOD return res def nPk(self, n, k): if k < 0 or k > n: return 0 return self.fact[n] * self.inv[n - k] % self.MOD def nHk(self, n, k): if k == 0: return 1 return self.__call__(n + k - 1, k) def __make_factorial_list(self, N): self.fact = [1] * (N + 1) self.inv = [1] * (N + 1) MOD = self.MOD for i in range(1, N + 1): self.fact[i] = (self.fact[i - 1] * i) % MOD self.inv[N] = pow(self.fact[N], MOD - 2, MOD) for i in range(N, 0, -1): self.inv[i - 1] = (self.inv[i] * i) % MOD return n, mod = map(int, input().split()) comb = Combination(n + 5, mod) fact = comb.fact inv = comb.inv div = [pow(i, mod-2, mod) for i in range(n + 1)] # dp[i, j]: 頂点iこ,辺jこ: 何通りか dp = [[0] * n for _ in range(n + 1)] dp[0][0] = 1 for i in range(1, n+1): dp[i][0] = dp[i-1][0] * (n - i + 1) * pow(i, mod-2, mod) % mod for i in range(2, n+1): # 連結成分の大きさiを並べる ndp = [[0] * n for _ in range(n + 1)] tree = pow(i, i-2, mod) for k in range(1, n+1): node = i * k if node > n: break edge = (i - 1) * k fi = pow(fact[i], k, mod) fi = pow(fi, mod-2, mod) ti = pow(tree, k, mod) for x in range(n - node + 1): choice = comb.nPk(n - x, node) * fi * ti % mod * inv[k] % mod for y in range(n - edge): ndp[x+node][y+edge] += dp[x][y] * choice ndp[x+node][y+edge] %= mod for j in range(n+1): for k in range(n): dp[j][k] += ndp[j][k] dp[j][k] %= mod for i in range(n): print(dp[n][i])