結果

問題 No.2720 Sum of Subarray of Subsequence of...
ユーザー ecotteaecottea
提出日時 2024-03-11 18:40:20
言語 PyPy3
(7.3.15)
結果
AC  
実行時間 859 ms / 4,000 ms
コード長 7,561 bytes
コンパイル時間 154 ms
コンパイル使用メモリ 81,700 KB
実行使用メモリ 143,892 KB
最終ジャッジ日時 2024-04-05 20:51:38
合計ジャッジ時間 13,028 ms
ジャッジサーバーID
（参考情報） 		judge15 / judge12
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テストケース

テストケース表示
入力 結果 実行時間
実行使用メモリ
testcase_00 AC 37 ms
55,596 KB
testcase_01 AC 36 ms
55,596 KB
testcase_02 AC 36 ms
55,596 KB
testcase_03 AC 40 ms
55,596 KB
testcase_04 AC 40 ms
55,596 KB
testcase_05 AC 40 ms
55,596 KB
testcase_06 AC 36 ms
55,596 KB
testcase_07 AC 38 ms
55,596 KB
testcase_08 AC 62 ms
73,160 KB
testcase_09 AC 66 ms
73,400 KB
testcase_10 AC 68 ms
74,028 KB
testcase_11 AC 72 ms
76,600 KB
testcase_12 AC 72 ms
76,472 KB
testcase_13 AC 60 ms
73,156 KB
testcase_14 AC 442 ms
112,332 KB
testcase_15 AC 689 ms
120,488 KB
testcase_16 AC 781 ms
125,288 KB
testcase_17 AC 747 ms
126,776 KB
testcase_18 AC 791 ms
129,188 KB
testcase_19 AC 859 ms
136,192 KB
testcase_20 AC 826 ms
136,576 KB
testcase_21 AC 763 ms
133,096 KB
testcase_22 AC 841 ms
137,604 KB
testcase_23 AC 762 ms
136,696 KB
testcase_24 AC 323 ms
110,640 KB
testcase_25 AC 37 ms
55,596 KB
testcase_26 AC 36 ms
55,596 KB
testcase_27 AC 515 ms
102,828 KB
testcase_28 AC 315 ms
108,000 KB
testcase_29 AC 308 ms
107,328 KB
testcase_30 AC 385 ms
119,396 KB
testcase_31 AC 853 ms
143,892 KB
testcase_32 AC 794 ms
137,840 KB
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ソースコード

diff # 

# https://judge.yosupo.jp/submission/55648 より拝借

########################### 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)

# 階乗とその逆数
fac = [1] * (m + 2)
for i in range(1, m + 2):
    fac[i] = (fac[i - 1] * i) % MOD

fac_inv = [1] * (m + 2)
fac_inv[m + 1] = pow(fac[m + 1], MOD - 2, MOD)
for i in range(m, 0, -1):
    fac_inv[i] = (fac_inv[i + 1] * (i + 1)) % MOD

# 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 i in range(1, K):
    if q[i] != 0:
        abs_q = abs(q[i])
        f = [0] * (abs_q + 1)
        i_pow = 1
        for k in range(0, abs_q + 1):
            f[k] = fac[abs_q] * fac_inv[abs_q - k] % MOD * fac_inv[k] % MOD * i_pow % MOD
            i_pow = i_pow * (MOD - i) % MOD
        if q[i] > 0:
            nums.append(f)
        else:
            dnms.append(f)

# 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)
0