from typing import List def bsf(x): res = 0 while not (x & 1): res += 1 x >>= 1 return res P = 943718401 G = 7 rank2 = bsf(P - 1) class NTT: class __RootInitializer: @staticmethod def root(): return [pow(G, (P - 1) >> i, P) for i in range(0, rank2 + 1)] @staticmethod def iroot(): return [pow(pow(G, P - 2, P), (P - 1) >> i, P) for i in range(0, rank2 + 1)] root = __RootInitializer.root() iroot = __RootInitializer.iroot() class __RateInitializer: @staticmethod def rates(root: List[int], iroot: List[int]): rate2 = [0] * max(0, rank2 - 1) irate2 = [0] * max(0, rank2 - 1) prod = iprod = 1 for i in range(rank2 - 1): rate2[i] = root[i + 2] * prod % P irate2[i] = iroot[i + 2] * iprod % P prod = prod * iroot[i + 2] % P iprod = iprod * root[i + 2] % P rate3 = [0] * max(0, rank2 - 2) irate3 = [0] * max(0, rank2 - 2) prod = iprod = 1 for i in range(rank2 - 2): rate3[i] = root[i + 3] * prod % P irate3[i] = iroot[i + 3] * iprod % P prod = prod * iroot[i + 3] % P iprod = iprod * root[i + 3] % P return rate2, irate2, rate3, irate3 rate2, irate2, rate3, irate3 = __RateInitializer.rates(__RootInitializer.root(), __RootInitializer.iroot()) @staticmethod def butterfly(a: List[int]) -> None: n = len(a) h = bsf(n) l = 0 while l < h: if h - l == 1: p = 1 << (h - l - 1) rot = 1 for s in range(1 << l): offset = s << (h - l) for i in range(p): u = a[i + offset] v = a[i + offset + p] * rot a[i + offset] = (u + v) % P a[i + offset + p] = (u - v) % P if s + 1 != 1 << l: rot = rot * NTT.rate2[bsf(~s)] % P l += 1 else: p = 1 << (h - l - 2) rot, imag = 1, NTT.root[2] for s in range(1 << l): rot2 = rot * rot % P rot3 = rot2 * rot % P offset = s << (h - l) for i in range(p): a0 = a[i + offset] a1 = a[i + offset + p] * rot a2 = a[i + offset + 2 * p] * rot2 a3 = a[i + offset + 3 * p] * rot3 a1na3imag = (a1 - a3) % P * imag a[i + offset] = (a0 + a2 + a1 + a3) % P a[i + offset + 1 * p] = (a0 + a2 - a1 - a3) % P a[i + offset + 2 * p] = (a0 - a2 + a1na3imag) % P a[i + offset + 3 * p] = (a0 - a2 - a1na3imag) % P if s + 1 != (1 << l): rot = rot * NTT.rate3[bsf(~s)] % P l += 2 @staticmethod def butterfly_inv(a : List[int]) -> None: n = len(a) h = bsf(n) l = h while l: if l == 1: p = 1 << (h - l) irot = 1 for s in range(1 << (l - 1)): offset = s << (h - l + 1) for i in range(p): u = a[i + offset] v = a[i + offset + p] a[i + offset] = (u + v) % P a[i + offset + p] = ((u - v) * irot) % P if s + 1 != 1 << (l - 1): irot = irot * NTT.irate2[bsf(~s)] % P l -= 1 else: p = 1 << (h - l) irot = 1 iimag = NTT.iroot[2] for s in range(1 << (l - 2)): irot2 = irot * irot % P irot3 = irot2 * irot % P offset = s << (h - l + 2) for i in range(p): a0 = a[i + offset] a1 = a[i + offset + p] a2 = a[i + offset + 2 * p] a3 = a[i + offset + 3 * p] a2na3iimag = (a2 - a3) * iimag % P a[i + offset] = (a0 + a1 + a2 + a3) % P a[i + offset + p] = ((a0 - a1 + a2na3iimag) * irot) % P a[i + offset + 2 * p] = ((a0 + a1 - a2 - a3) * irot2) % P a[i + offset + 3 * p] = ((a0 - a1 - a2na3iimag) * irot3) % P if s + 1 != 1 << (l - 2): irot = irot * NTT.irate3[bsf(~s)] % P l -= 2 @staticmethod def convolution(a, b): n = len(a) m = len(b) if not a or not b: return [] if min(n, m) <= 40: if n < m: n, m = m, n a, b = b, a res = [0] * (n + m - 1) for i in range(n): for j in range(m): res[i + j] += a[i] * b[j] res[i + j] %= P return res z = 1 << ((n + m - 1).bit_length()) iz = pow(z, P - 2, P) a += [0] * (z - n) b += [0] * (z - m) NTT.butterfly(a) NTT.butterfly(b) c = [a[i] * b[i] % P * iz % P for i in range(z)] NTT.butterfly_inv(c) return c[:n + m - 1] n, x = map(int, input().split()) A = list(map(int, input().split())) B = list(map(int, input().split())) C = list(map(int, input().split())) if x == 0: ans = sum(A[i] * B[i] % P * C[0] % P for i in range(n + 1)) + sum(A[i] * B[0] % P * C[i] % P for i in range(1, n + 1)) print(ans % P) else: def enumerate_powers(x, n): x2 = x * x % P pow_x2 = 1 # x ** (2i) y = 1 # x ** (i(i + 1)) z = 1 # x ** t(i) yield z for _ in range(n): yield z pow_x2 = pow_x2 * x2 % P y = y * pow_x2 % P z = z * y % P t = lambda k : (k - 1) * k * (k + 1) // 3 inv_x = pow(x, P - 2, P) pows_inv_x = list(enumerate_powers(inv_x, n)) pows_x = list(enumerate_powers(x, n)) F = [B[i] * pows_inv_x[i] % P for i in range(n + 1)] G = [C[i] * pows_inv_x[i] % P for i in range(n + 1)] H = NTT.convolution(F, G) ans = sum(A[i] * pows_x[i] % P * H[i] % P for i in range(n + 1)) print(ans % P)