MOD = 998244353 class Matrix(): def __init__(self, n, m, mat=None): self.n = n self.m = m self.mat = [[0] * self.m for _ in range(self.n)] if mat: assert len(mat) == n and len(mat[0]) == m for i in range(self.n): self.mat[i] = mat[i].copy() def is_square(self): return self.n == self.m def __getitem__(self, key): if isinstance(key, slice): return self.mat[key] else: assert key >= 0 return self.mat[key] def id(n): res = Matrix(n, n) for i in range(n): res[i][i] = 1 return res def __len__(self): return len(self.mat) def __str__(self): return '\n'.join(' '.join(map(str, self[i])) for i in range(self.n)) def times(self, k): res = [[0] * self.m for _ in range(self.n)] for i in range(self.n): res_i, self_i = res[i], self[i] for j in range(self.m): res_i[j] = k * self_i[j] % MOD return Matrix(self.n, self.m, res) def __pos__(self): return self def __neg__(self): return self.times(-1) def __add__(self, other): assert self.n == other.n and self.m == other.m res = [[0] * self.m for _ in range(self.n)] for i in range(self.n): res_i, self_i, other_i = res[i], self[i], other[i] for j in range(self.m): res_i[j] = (self_i[j] + other_i[j]) % MOD return Matrix(self.n, self.m, res) def __sub__(self, other): assert self.n == other.n and self.m == other.m res = [[0] * self.m for _ in range(self.n)] for i in range(self.n): res_i, self_i, other_i = res[i], self[i], other[i] for j in range(self.m): res_i[j] = (self_i[j] - other_i[j]) % MOD return Matrix(self.n, self.m, res) def __mul__(self, other): if other.__class__ == Matrix: assert self.m == other.n res = [[0] * other.m for _ in range(self.n)] for i in range(self.n): res_i, self_i = res[i], self[i] for k in range(self.m): self_ik, other_k = self_i[k], other[k] for j in range(other.m): res_i[j] += self_ik * other_k[j] res_i[j] %= MOD return Matrix(self.n, other.m, res) elif other.__class__ == list: assert self.m == len(other) res = [0] * self.n for i in range(self.n): self_i = self[i] for j in range(self.m): res[i] += self_i[j] * other[j] res[i] %= MOD return res else: return self.times(other) def __rmul__(self, other): return self.times(other) def __pow__(self, k): assert self.is_square() tmp = Matrix(self.n, self.n, self.mat) res = Matrix.id(self.n) while k: if k & 1: res *= tmp tmp *= tmp k >>= 1 return res n, k = map(int, input().split()) mat = [[0] * (k * k) for _ in range(k * k)] for i in range(k): for j in range(i + 1, k): for p in range(j): if i == p: continue mat[j + p * k][i + j * k] = 1 for i in range(k): for j in range(i): for p in range(j + 1, k): if i == p: continue mat[j + p * k][i + j * k] = 1 f1 = Matrix(k * k, k * k, mat) a = [0] * (k * k) for i in range(k): for j in range(k): if i != j: a[i * k + j] = 1 ans1 = sum(f1 ** (n - 2) * a) % MOD ans2 = ans1 * n * (k - 1) * pow(2, MOD - 2, MOD) % MOD print(ans1, ans2)