# https://judge.yosupo.jp/submission/55648 より拝借しました． ########################### ここから ########################### # AtCoder Libary v1.4 を python に移植したもの # https://github.com/atcoder/ac-library/blob/master/atcoder/convolution.hpp MOD = 998244353 IMAG = 911660635 IIMAG = 86583718 rate2 = (0, 911660635, 509520358, 369330050, 332049552, 983190778, 123842337, 238493703, 975955924, 603855026, 856644456, 131300601, 842657263, 730768835, 942482514, 806263778, 151565301, 510815449, 503497456, 743006876, 741047443, 56250497, 867605899, 0) irate2 = (0, 86583718, 372528824, 373294451, 645684063, 112220581, 692852209, 155456985, 797128860, 90816748, 860285882, 927414960, 354738543, 109331171, 293255632, 535113200, 308540755, 121186627, 608385704, 438932459, 359477183, 824071951, 103369235, 0) rate3 = (0, 372528824, 337190230, 454590761, 816400692, 578227951, 180142363, 83780245, 6597683, 70046822, 623238099, 183021267, 402682409, 631680428, 344509872, 689220186, 365017329, 774342554, 729444058, 102986190, 128751033, 395565204, 0) irate3 = (0, 509520358, 929031873, 170256584, 839780419, 282974284, 395914482, 444904435, 72135471, 638914820, 66769500, 771127074, 985925487, 262319669, 262341272, 625870173, 768022760, 859816005, 914661783, 430819711, 272774365, 530924681, 0) def butterfly(a): n = len(a) h = (n - 1).bit_length() le = 0 while le < h: if h - le == 1: p = 1 << (h - le - 1) rot = 1 for s in range(1 << le): offset = s << (h - le) for i in range(p): l = a[i + offset] r = a[i + offset + p] * rot a[i + offset] = (l + r) % MOD a[i + offset + p] = (l - r) % MOD rot *= rate2[(~s & -~s).bit_length()] rot %= MOD le += 1 else: p = 1 << (h - le - 2) rot = 1 for s in range(1 << le): rot2 = rot * rot % MOD rot3 = rot2 * rot % MOD offset = s << (h - le) for i in range(p): a0 = a[i + offset] a1 = a[i + offset + p] * rot a2 = a[i + offset + p * 2] * rot2 a3 = a[i + offset + p * 3] * rot3 a1na3imag = (a1 - a3) % MOD * IMAG a[i + offset] = (a0 + a2 + a1 + a3) % MOD a[i + offset + p] = (a0 + a2 - a1 - a3) % MOD a[i + offset + p * 2] = (a0 - a2 + a1na3imag) % MOD a[i + offset + p * 3] = (a0 - a2 - a1na3imag) % MOD rot *= rate3[(~s & -~s).bit_length()] rot %= MOD le += 2 def butterfly_inv(a): n = len(a) h = (n - 1).bit_length() le = h while le: if le == 1: p = 1 << (h - le) irot = 1 for s in range(1 << (le - 1)): offset = s << (h - le + 1) for i in range(p): l = a[i + offset] r = a[i + offset + p] a[i + offset] = (l + r) % MOD a[i + offset + p] = (l - r) * irot % MOD irot *= irate2[(~s & -~s).bit_length()] irot %= MOD le -= 1 else: p = 1 << (h - le) irot = 1 for s in range(1 << (le - 2)): irot2 = irot * irot % MOD irot3 = irot2 * irot % MOD offset = s << (h - le + 2) for i in range(p): a0 = a[i + offset] a1 = a[i + offset + p] a2 = a[i + offset + p * 2] a3 = a[i + offset + p * 3] a2na3iimag = (a2 - a3) * IIMAG % MOD a[i + offset] = (a0 + a1 + a2 + a3) % MOD a[i + offset + p] = (a0 - a1 + a2na3iimag) * irot % MOD a[i + offset + p * 2] = (a0 + a1 - a2 - a3) * irot2 % MOD a[i + offset + p * 3] = (a0 - a1 - a2na3iimag) * irot3 % MOD irot *= irate3[(~s & -~s).bit_length()] irot %= MOD le -= 2 def multiply(s, t): n = len(s) m = len(t) if min(n, m) <= 60: a = [0] * (n + m - 1) for i in range(n): if i % 8 == 0: for j in range(m): a[i + j] += s[i] * t[j] a[i + j] %= MOD else: for j in range(m): a[i + j] += s[i] * t[j] return [x % MOD for x in a] a = s.copy() b = t.copy() z = 1 << (n + m - 2).bit_length() a += [0] * (z - n) b += [0] * (z - m) butterfly(a) butterfly(b) for i in range(z): a[i] *= b[i] a[i] %= MOD butterfly_inv(a) a = a[:n + m - 1] iz = pow(z, MOD - 2, MOD) return [v * iz % MOD for v in a] import atexit import os import sys import __pypy__ class Fastio: def __init__(self): self.ibuf = bytes() self.pil = 0 self.pir = 0 self.sb = __pypy__.builders.StringBuilder() def load(self): self.ibuf = self.ibuf[self.pil:] self.ibuf += os.read(0, 131072) self.pil = 0 self.pir = len(self.ibuf) def flush(self): os.write(1, self.sb.build().encode()) def fastin(self): if self.pir - self.pil < 32: self.load() minus = 0 x = 0 while self.ibuf[self.pil] < 45: self.pil += 1 if self.ibuf[self.pil] == 45: minus = 1 self.pil += 1 while self.ibuf[self.pil] >= 48: x = x * 10 + (self.ibuf[self.pil] & 15) self.pil += 1 if minus: x = -x return x def fastout(self, x): self.sb.append(str(x)) def fastoutln(self, x): self.sb.append(str(x)) self.sb.append('\n') ########################### ここまで ########################### from collections import deque n, m = map(int, input().split()) a = list(map(int, input().split())) s = input() MOD = 998244353 # g_j(x) を (1-x)^(e_1) (1-2x)^(e_2) (1-3x)^(e_3) ... と表したときの指数列を更新していく． q = deque() q.append(-1) q_sum = -1 for i in range(m): if s[i] == 's': q.appendleft(-q_sum - 1) q_sum = -1 elif s[i] == 'a': q[0] -= 1 q_sum -= 1 q.appendleft(0) K = len(q) # g_M(x) の (1-kx) たちを分子と分母に振り分ける． nums = [[1]] dnms = [[1]] for k in range(1, K): if q[k] > 0: for _ in range(q[k]): nums.append([1, -k]) elif q[k] < 0: for _ in range(-q[k]): dnms.append([1, -k]) # 分子を分割統治法で求める． Dnum = len(nums) d = 1 while (d < Dnum): for i in range(0, Dnum - d, 2 * d): nums[i] = multiply(nums[i], nums[i + d]) d <<= 1 # 分母を分割統治法で求める． Ddnm = len(dnms) d = 1 while (d < Ddnm): for i in range(0, Ddnm - d, 2 * d): dnms[i] = multiply(dnms[i], dnms[i + d]) d <<= 1 # 分母の形式的冪級数としての逆元を求める． while len(dnms[0]) > n: dnms[0].pop() while len(dnms[0]) < n: dnms[0].append(0) dnm_inv = [1] k = 1 while (k < n): l = min(2 * k, n) tmp = [0] * l i_ub = min(l, n) for i in range(i_ub): tmp[i] = -dnms[0][i] tmp = multiply(tmp, dnm_inv) while len(tmp) > l: tmp.pop() tmp[0] += 2 dnm_inv = multiply(tmp, dnm_inv) while len(dnm_inv) > l: dnm_inv.pop() k <<= 1 # g_M(x) を求める． f = multiply(nums[0], dnm_inv) # 答えへの寄与を足し合わせる． res = 0 for i in range(n): l = i r = n - 1 - i res = (res + a[i] * f[l] % MOD * f[r] % MOD) % MOD print(res)