## https://yukicoder.me/problems/no/707 MOD = 998244353 class NTT: def __init__(self): self._root = self._make_root() self._invroot = self._make_invroot(self._root) def _reverse_bits(self, n): n = (n >> 16) | (n << 16) n = ((n & 0xff00ff00) >> 8) | ((n & 0x00ff00ff) << 8) n = ((n & 0xf0f0f0f0) >> 4) | ((n & 0x0f0f0f0f) << 4) n = ((n & 0xcccccccc) >> 2) | ((n & 0x33333333) << 2) n = ((n & 0xaaaaaaaa) >> 1) | ((n & 0x55555555) << 1) return n def _make_root(self): # 3はMODの原始根, 119乗するとconvolusion, NTT における「基底」の条件を満たす r = pow(3, 119, MOD) return [pow(r, 2 ** i, MOD) for i in range(23, -1, -1)] def _make_invroot(self, root): invroot = [] for i in range(len(root)): invroot.append(pow(root[i], MOD - 2, MOD)) return invroot def _ntt(self, poly, root, rev, max_l): n = len(poly) k = (n - 1).bit_length() step = (max_l) >> k for i, j in enumerate(rev[::step]): if i < j: poly[i], poly[j] = poly[j], poly[i] r = 1 for w in root[1:(k + 1)]: for l in range(0, n, r * 2): wi = 1 for i in range(r): a = (poly[l + i + r] * wi) % MOD a += poly[l + i] a %= MOD b = (-poly[l + i + r] * wi) % MOD b += poly[l + i] b %= MOD poly[l + i] = a poly[l + i + r] = b wi *= w wi %= MOD r <<= 1 def convolution(self, poly_l, poly_r): # 多項式を畳み込んだ時の次数よりも大きい2の冪の長さを求める # (NTTの特性上2の冪乗に乗せるため) len_ans = len(poly_l) + len(poly_r) - 1 if (min(len(poly_l), len(poly_r)) <= 40): return self._combolution_light(poly_l, poly_r) # 2の冪の長さを求める n = 1 max_depth = 0 while n <= len_ans: n *= 2 max_depth += 1 rev = [self._reverse_bits(i) >> (32- max_depth) for i in range(n)] new_poly_l = [0] * n for i in range(len(poly_l)): new_poly_l[i] = poly_l[i] new_poly_r = [0] * n for i in range(len(poly_r)): new_poly_r[i] = poly_r[i] # 数論変換 self._ntt(new_poly_l, self._root, rev, n) self._ntt(new_poly_r, self._root, rev, n) # 畳み込みは各iを代入した値の積で求められる d_ans = [0] * n for i in range(n): d_ans[i] = (new_poly_l[i] * new_poly_r[i]) % MOD # 逆数論変換 self._ntt(d_ans, self._invroot, rev, n) # 最後の定数分割る処理 inv_n = pow(n, MOD - 2, MOD) poly_ans = [0] * len_ans for i in range(len_ans): poly_ans[i] = (d_ans[i] * inv_n) % MOD return poly_ans def _combolution_light(self, poly_l, poly_r): poly_ans = [0] * (len(poly_l) + len(poly_r) - 1) for i in range(len(poly_l)): for j in range(len(poly_r)): poly_ans[i + j] += (poly_l[i] * poly_r[j]) % MOD poly_ans[i + j] %= MOD return poly_ans def main(): N, K = map(int, input().split()) A = list(map(int, input().split())) if N == 1: print(A[0]) return K_ = K // 2 a_even = [] a_odd = [] for i in range(N): if i % 2 == 0: a_even.append(A[i]) else: a_odd.append(A[i]) combi = [0] * (N + 1) b = 1 k = K_ c = 1 for i in range(N + 1): combi[i] = b b *= k b %= MOD k -= 1 c += 1 # even n_e = (N + 1) // 2 base_poly = [0] * n_e for l in range(n_e): base_poly[l] = combi[l] ntt = NTT() even_poly = ntt.convolution(a_even, base_poly) even_poly = even_poly[:(n_e + 1)] # odd n_o = N // 2 base_poly = [0] * n_o for l in range(n_o): base_poly[l] = combi[l] odd_poly = ntt.convolution(a_odd, base_poly) odd_poly = odd_poly[:(n_o + 1)] A_ = [0] * N for i in range(N): if i % 2 == 0: A_[i] = even_poly[i // 2] else: A_[i] = odd_poly[i // 2] answer = [0] * N if K % 2 == 0: answer = A_ else: a = 0 for i in range(N): if i % 2 == 0: a += A_[i] a %= MOD else: a -= A_[i] a %= MOD answer[i] = a print(" ".join(map(str, answer))) if __name__ == "__main__": main()