結果

問題 No.2959 Dolls' Tea Party
ユーザー PNJPNJ
提出日時 2024-11-08 23:55:00
言語 PyPy3
(7.3.15)
結果
AC  
実行時間 2,457 ms / 3,000 ms
コード長 9,011 bytes
コンパイル時間 216 ms
コンパイル使用メモリ 82,176 KB
実行使用メモリ 137,408 KB
最終ジャッジ日時 2024-11-08 23:56:12
合計ジャッジ時間 68,920 ms
ジャッジサーバーID
（参考情報） 		judge4 / judge1
このコードへのチャレンジ
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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 60 ms
63,616 KB
testcase_01 AC 61 ms
64,384 KB
testcase_02 AC 61 ms
63,616 KB
testcase_03 AC 69 ms
66,560 KB
testcase_04 AC 62 ms
64,128 KB
testcase_05 AC 61 ms
64,000 KB
testcase_06 AC 2,363 ms
131,644 KB
testcase_07 AC 2,432 ms
136,732 KB
testcase_08 AC 2,388 ms
137,408 KB
testcase_09 AC 2,375 ms
122,116 KB
testcase_10 AC 2,390 ms
120,700 KB
testcase_11 AC 2,376 ms
122,112 KB
testcase_12 AC 2,382 ms
121,192 KB
testcase_13 AC 2,395 ms
120,592 KB
testcase_14 AC 2,353 ms
137,272 KB
testcase_15 AC 2,436 ms
137,296 KB
testcase_16 AC 2,387 ms
122,052 KB
testcase_17 AC 2,387 ms
122,440 KB
testcase_18 AC 2,396 ms
122,436 KB
testcase_19 AC 2,406 ms
123,920 KB
testcase_20 AC 2,392 ms
122,312 KB
testcase_21 AC 2,451 ms
122,636 KB
testcase_22 AC 2,457 ms
122,896 KB
testcase_23 AC 2,452 ms
122,516 KB
testcase_24 AC 58 ms
63,360 KB
testcase_25 AC 59 ms
63,232 KB
testcase_26 AC 59 ms
63,488 KB
testcase_27 AC 2,387 ms
105,748 KB
testcase_28 AC 2,377 ms
105,752 KB
testcase_29 AC 2,379 ms
121,812 KB
testcase_30 AC 2,287 ms
121,272 KB
testcase_31 AC 2,315 ms
121,552 KB
testcase_32 AC 2,217 ms
120,452 KB
testcase_33 AC 2,366 ms
120,836 KB
testcase_34 AC 2,376 ms
121,832 KB
testcase_35 AC 2,387 ms
121,072 KB
testcase_36 AC 2,180 ms
122,396 KB
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ソースコード

diff # 

def make_divisors(n):
  lower_divisors , upper_divisors = [], []
  i = 1
  while i*i < n:
    if n % i == 0:
      lower_divisors.append(i)
      if i != n // i:
        upper_divisors.append(n//i)
    i += 1
  if i * i == n:
    lower_divisors.append(i)
  return lower_divisors + upper_divisors[::-1]

def gcd(a, b):
  while a != 0:
    b %= a
    if b == 0: return a
    a %= b
  return b

mod = 998244353
n = 10000
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

fact = [1 for i in range(n + 1)]
for i in range(1,n + 1):
  fact[i] = fact[i - 1] * i % mod

fact_inv = [1 for i in range(n + 1)]
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

NTT_friend = [120586241,167772161,469762049,754974721,880803841,924844033,943718401,998244353,1045430273,1051721729,1053818881]
NTT_dict = {}
for i in range(len(NTT_friend)):
  NTT_dict[NTT_friend[i]] = i
NTT_info = [[20,74066978],[25,17],[26,30],[24,362],[23,211],[21,44009197],[22,663003469],[23,31],[20,363],[20,330],[20,2789]]

def popcount(n):
  c = (n&0x5555555555555555) + ((n>>1)&0x5555555555555555)
  c = (c&0x3333333333333333) + ((c>>2)&0x3333333333333333)
  c = (c&0x0f0f0f0f0f0f0f0f) + ((c>>4)&0x0f0f0f0f0f0f0f0f)
  c = (c&0x00ff00ff00ff00ff) + ((c>>8)&0x00ff00ff00ff00ff)
  c = (c&0x0000ffff0000ffff) + ((c>>16)&0x0000ffff0000ffff)
  c = (c&0x00000000ffffffff) + ((c>>32)&0x00000000ffffffff)
  return c

def topbit(n):
  h = n.bit_length()
  h -= 1
  return h

def prepared_fft(mod = 998244353):
  rank2 = NTT_info[NTT_dict[mod]][0]
  root,iroot = [0] * 30,[0] * 30
  rate2,irate2= [0] * 30,[0] * 30
  rate3,irate3= [0] * 30,[0] * 30

  root[rank2] = NTT_info[NTT_dict[mod]][1]
  iroot[rank2] = pow(root[rank2],mod - 2,mod)
  for i in range(rank2 - 1,-1,-1):
    root[i] = root[i + 1] * root[i + 1] % mod
    iroot[i] = iroot[i + 1] * iroot[i + 1] % mod

  prod,iprod = 1,1
  for i in range(rank2-1):
    rate2[i] = root[i + 2] * prod % mod
    irate2[i] = iroot[i + 2] * iprod % mod
    prod = prod * iroot[i + 2] % mod
    iprod = iprod * root[i + 2] % mod
  
  prod,iprod = 1,1
  for i in range(rank2-2):
    rate3[i] = root[i + 3] * prod % mod
    irate3[i] = iroot[i + 3] * iprod % mod
    prod = prod * iroot[i + 3] % mod
    iprod = iprod * root[i + 3] % mod
  
  return root,iroot,rate2,irate2,rate3,irate3

root,iroot,rate2,irate2,rate3,irate3 = prepared_fft()

def ntt(a):
  n = len(a)
  h = topbit(n)
  assert (n == 1 << h)
  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 % mod
          a[i + offset] = (l + r) % mod
          a[i + offset + p] = (l - r) % mod
        rot = rot * rate2[topbit(~s & -~s)] % mod
      le += 1
    else:
      p = 1 << (h - le - 2)
      rot,imag = 1,root[2]
      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 = rot * rate3[topbit(~s & -~s)] % mod
      le += 2

def intt(a):
  n = len(a)
  h = topbit(n)
  assert (n == 1 << h)
  coef = inv[n]
  for i in range(n):
    a[i] = a[i] * coef % mod
  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 = irot * irate2[topbit(~s & -~s)] % mod
      le -= 1
    else:
      p = 1 << (h - le)
      irot,iimag = 1,iroot[2]
      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[topbit(~s & -~s)]
        irot %= mod
      le -= 2

def convolute_naive(a,b):
  res = [0] * (len(a) + len(b) - 1)
  for i in range(len(a)):
    for j in range(len(b)):
      res[i + j] = (res[i + j] + a[i] * b[j] % mod) % mod
  return res

def convolute(a,b):
  s = a[:]
  t = b[:]
  n = len(s)
  m = len(t)
  if min(n,m) <= 30:
    return convolute_naive(a,b)
  le = 1
  while le < n + m - 1:
    le *= 2
  s += [0] * (le - n)
  t += [0] * (le - m)
  ntt(s)
  ntt(t)
  for i in range(le):
    s[i] = s[i] * t[i] % mod
  intt(s)
  s = s[:n + m - 1]
  return s

def fps_inv(f,deg = -1):
  if deg == -1:
    deg = len(f)
  res = [0] * deg
  res[0] = 1
  d = 1
  while d < deg:
    a = [0] * (d << 1)
    tmp = min(len(f),d << 1)
    a[:tmp] = f[:tmp]
    b = [0] * (d << 1)
    b[:d] = res[:d]
    ntt(a)
    ntt(b)
    for i in range(d << 1):
      a[i] = a[i] * b[i] % mod
    intt(a)
    a[:d] = [0] * d
    ntt(a)
    for i in range(d << 1):
      a[i] = a[i] * b[i] % mod
    intt(a)
    for j in range(d,min(d << 1,deg)):
      if a[j]:
        res[j] = mod - a[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_add(f,g):
  n = max(len(f),len(g))
  res = [0] * n
  for i in range(len(f)):
    res[i] = f[i]
  for i in range(len(g)):
    res[i] = (res[i] + g[i]) % mod
  return res

def fps_diff(f):
  if len(f) <= 1:
    return [0]
  res = []
  for i in range(1,len(f)):
    res.append(i * f[i] % mod)
  return res

def fps_integrate(f):
  n = len(f)
  res = [0] * (n + 1)
  for i in range(n):
    res[i + 1] = inv[i + 1] * f[i] % mod
  return res

def fps_log(f,deg = -1):
  assert (f[0] == 1)
  if deg == -1:
    deg = len(f)
  res = convolute(fps_diff(f),fps_inv(f,deg))[:deg - 1]
  res = fps_integrate(res)
  return res

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

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

D = make_divisors(K)
M = len(D)
dic = {}
for i in range(M):
  dic[D[i]] = i

LOG = [[]]
g = [1]
for i in range(1,K + 1):
  g.append(fact_inv[i])
  gg = fps_log(g,K + 1)
  LOG.append(gg)

C = []
for d in D:
  n = K // d
  Q = [0 for i in range(n + 1)]
  for i in range(1,K + 1):
    Q[min(i // d,n)] += P[i]
  f = [0 for j in range(n + 1)]
  f[1] = sum(Q) - Q[0]
  for i in range(1,n):
    if Q[i] == 0:
      continue
    for j in range(i + 1,n + 1):
      f[j] = (f[j] + LOG[i][j] * Q[i] % mod) % mod
  f = fps_exp(f)
  C.append(f[n] * fact[n] % mod)

res = 0
for k in range(1,K + 1):
  g = gcd(k,K)
  d = K // g
  res += C[dic[d]]
  res %= mod

res = res * inv[K] % mod
print(res)
0