#987710 (PyPy3) No.1145 Sums of Powers

提出ソース

結果

問題	No.1145 Sums of Powers
ユーザー	PNJ
提出日時	2024-06-10 20:48:24
言語	PyPy3 (7.3.15)
結果	AC
実行時間	1,051 ms / 2,000 ms
コード長	5,667 bytes
コンパイル時間	298 ms
コンパイル使用メモリ	82,364 KB
実行使用メモリ	139,244 KB
最終ジャッジ日時	2024-06-10 20:48:29
合計ジャッジ時間	4,622 ms
ジャッジサーバーID （参考情報）	judge3 / judge5

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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	38 ms 56,272 KB
testcase_01	AC	39 ms 57,112 KB
testcase_02	AC	141 ms 78,144 KB
testcase_03	AC	1,051 ms 138,520 KB
testcase_04	AC	1,040 ms 139,244 KB
testcase_05	AC	1,045 ms 138,328 KB

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ソースコード

raw source code

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 fft(a):
  n = len(a)
  h = (n - 1).bit_length()
  le = 0
  while le < h:
    if h == le + 1:
      p = 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 fft_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 ntt(a):
  if len(a) <= 1:
    return
  fft(a)

def ntt_inv(a):
  if len(a) <= 1:
    return
  fft_inv(a)
  iv = pow(len(a),mod-2,mod)
  for i in range(len(a)):
    a[i] = a[i] * iv % mod

def convolute(s, t):
  a = s[:]
  b = t[:]
  n = len(a)
  m = len(b)
  z = 1 << (n + m - 2).bit_length()
  a += [0] * (z - n)
  b += [0] * (z - m)
  fft(a)
  fft(b)
  for i in range(z):
    a[i] *= b[i]
    a[i] %= mod
  fft_inv(a)
  a = a[:n + m - 1]
  iz = pow(z, mod - 2, mod)
  for i in range(n+m-1):
    a[i] = (a[i] * iz) % mod
  return a

def fps_inv(a,deg = -1):
  if deg == -1:
    deg = len(a)
  res = [0] * deg
  res[0] = pow(a[0],mod-2,mod)
  d = 1
  while d < deg:
    f = [0] * (d << 1)
    tmp = min(len(a),d << 1)
    f[:tmp] = a[:tmp]
    g = [0] * (d << 1)
    g[:d] = res[:d]
    ntt(f)
    ntt(g)
    for i in range(d << 1):
      f[i] = f[i] * g[i] % mod
    ntt_inv(f)
    f[:d] = [0] * d
    ntt(f)
    for i in range(d << 1):
      f[i] = f[i] * g[i] % mod
    ntt_inv(f)
    for j in range(d,min(d << 1,deg)):
      if f[j]:
        res[j] = mod - f[j]
      else:
        res[j] = 0
    d <<= 1
  return res

def fps_div(f,g):
  n,m = len(f),len(g)
  if n < m:
    return [],f
  rev_f = f[:]
  rev_f = rev_f[::-1]
  rev_g = g[:]
  rev_g = rev_g[::-1]
  rev_q = convolute(rev_f,fps_inv(rev_g,n-m+1))[:n-m+1]
  q = rev_q[:]
  q = q[::-1]
  p = convolute(g,q)
  r = f[:]
  for i in range(min(len(p),len(r))):
    r[i] -= p[i]
    r[i] %= mod
  while len(r):
    if r[-1] != 0:
      break
    r.pop()
  return q,r

def fps_diff(a):
  res = []
  for i in range(1,len(a)):
    res.append(i * a[i] % mod)
  return res

def fps_integrate(a):
  n = len(a)
  res = [0] * (n + 1)
  for i in range(n):
    res[i+1] = pow(i + 1,mod-2,mod) * a[i] % mod
  return res

def fps_log(a,deg = -1):
  if deg == -1:
    deg = len(a)
  res = convolute(fps_diff(a),fps_inv(a,deg))
  res = fps_integrate(res)
  return res[:deg]

from collections import deque

N,M = map(int,input().split())
A = list(map(int,input().split()))
F = deque([[1,-A[i]] for i in range(N)])
while len(F) > 1:
  f = F.popleft()
  g = F.popleft()
  h = convolute(f,g)
  F.append(h)
F = F[0]
F = fps_log(F,M+1)
F = fps_diff(F)
for i in range(len(F)):
  F[i] = (mod - F[i]) % mod
print(*F)

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結果

テストケース

ソースコード