結果

問題 No.2243 Coaching Schedule
コンテスト
ユーザー PNJ
提出日時 2024-05-16 21:06:43
言語 PyPy3
(7.3.15)
結果
AC  
実行時間 1,881 ms / 4,000 ms
コード長 8,684 bytes
コンパイル時間 351 ms
コンパイル使用メモリ 81,912 KB
実行使用メモリ 94,528 KB
最終ジャッジ日時 2024-12-20 11:09:08
合計ジャッジ時間 18,654 ms
ジャッジサーバーID
（参考情報） 		judge5 / judge1
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ファイルパターン 結果
other AC * 37
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ソースコード

diff # 

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]

def fps_exp(a,deg = -1):
  if deg == -1:
    deg = len(a)
  b = [1,0]
  if len(a) > 1:
    b[1] = a[1]
  c = [1]
  p = []
  q = [1,1]
  m = 2
  while m < deg:
    y = b + [0]*m
    ntt(y)
    p = q
    z = [y[i] * p[i] for i in range(len(p))]
    ntt_inv(z)
    z[:m >> 1] = [0] * (m >> 1)
    ntt(z)
    for i in range(len(p)):
      z[i] = z[i] * (-p[i]) % mod
    ntt_inv(z)
    c[m >> 1:] = z[m >> 1:]
    q = c + [0] * m
    ntt(q)
    tmp = min(len(a),m)
    x = a[:tmp] + [0] * (m - tmp)
    x = fps_diff(x)
    x.append(0)
    ntt(x)
    for i in range(len(x)):
      x[i] = x[i] * y[i] % mod
    ntt_inv(x)
    for i in range(len(b)):
      if i == 0:
        continue
      x[i-1] -= b[i] * i % mod
    x += [0] * m
    for i in range(m-1):
      x[m+i],x[i] = x[i],0
    ntt(x)
    for i in range(len(q)):
      x[i] = x[i] * q[i] % mod
    ntt_inv(x)
    x.pop()
    x = fps_integrate(x)
    x[:m] = [0] * m
    for i in range(m,min(len(a),m << 1)):
      x[i] += a[i]
    ntt(x)
    for i in range(len(y)):
      x[i] = x[i] * y[i] % mod
    ntt_inv(x)
    b[m:] = x[m:]
    m <<= 1
  return b[:deg]

def fps_pow(f,k,deg = -1):
  if k == 0:
    return [1] + [0] * (len(f) - 1)
  p = 0
  if deg == -1:
    deg = len(f)
  while p < deg:
    if f[p]:
      break
    p += 1
  if p == deg:
    return [0] * len(f)
  a = f[p]
  a_inv = pow(a,mod-2,mod)
  a = pow(a,k,mod)
  f = f[p:]
  for i in range(deg-p):
    f[i] = f[i] * a_inv % mod
  g = fps_log(f)
  for i in range(deg-p):
    g[i] = g[i] * k % mod
  g = fps_exp(g)
  res = [0] * deg
  for i in range(deg):
    j = i + p*k
    if j >= deg:
      break
    res[j] = g[i] * a % mod
  return res

def Bostan_Mori(N,Q,A = [1]):
  d = len(Q) - 1
  P = convolute(Q,A)[:d]
  n = N
  while True:
    if n == 0:
      return P[0]
    QQ = [Q[i] for i in range(d+1)]
    for i in range(1,d+1,2):
      QQ[i] = mod - QQ[i]
    UU = convolute(P,QQ)
    U_e = []
    U_o = []
    for i in range(len(UU)):
      if i % 2:
        U_o.append(UU[i])
      else:
        U_e.append(UU[i])
    V = convolute(Q,QQ)
    Q = [V[2*i] for i in range(d+1)]
    if n % 2:
      P = U_o[:]
    else:
      P = U_e[:]
    n //= 2

n = 10**5
fact = [1 for i in range(n+1)]
fact_inv = [1 for i in range(n+1)]
for i in range(1,n+1):
  fact[i] = fact[i-1]*i % mod
fact_inv[-1] = pow(fact[-1],mod-2,mod)
for i in range(n,0,-1):
  fact_inv[i-1] = fact_inv[i]*i % mod
def comb(n,r):
  if n < r or n < 0 or r < 0:
    return 0
  res = fact_inv[n-r] * fact_inv[r] % mod
  res *= fact[n]
  res %= mod
  return res
inv = [1 for j in range(n+1)]
for a in range(2,n+1):
  # ax + py = 1 <=> rx + p(-x-qy) = -q => x = -(inv[r]) * (p//a)  (r = p % a)
  res = (mod - inv[mod%a]) * (mod // a)
  inv[a] = res % mod

M,N = map(int,input().split())
A = list(map(int,input().split()))
C = [0 for i in range(M+1)]
for a in A:
  C[a] += 1

D = [0 for i in range(N+1)]
for c in C:
  D[c] += 1

F = [fact_inv[i] for i in range(N+1)]
for c in range(N+1):
  if D[c] == 0:
    continue
  for n in range(N+1):
    if n < c:
      F[n] = 0
    else:
      f = pow(fact[n] * fact_inv[n-c] % mod,D[c],mod)
      F[n] = F[n] * f % mod

G = [fact_inv[i] for i in range(N+1)]
for i in range(N):
  if i % 2:
    G[i] = mod - G[i]

H = convolute(F,G)

ans = 0
for n in range(N+1):
  H[n] = H[n] * fact[n] % mod
  ans += H[n]
  ans %= mod
print(ans)
0