結果

問題 No.2917 二重木
ユーザー PNJPNJ
提出日時 2024-10-04 22:29:51
言語 PyPy3
(7.3.15)
結果
WA  
実行時間 -
コード長 10,554 bytes
コンパイル時間 259 ms
コンパイル使用メモリ 82,224 KB
実行使用メモリ 94,300 KB
最終ジャッジ日時 2024-10-04 22:30:25
合計ジャッジ時間 29,056 ms
ジャッジサーバーID
（参考情報） 		judge1 / judge3
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 39 ms
56,008 KB
testcase_01 AC 40 ms
56,916 KB
testcase_02 AC 41 ms
56,596 KB
testcase_03 AC 39 ms
55,732 KB
testcase_04 AC 39 ms
57,036 KB
testcase_05 AC 38 ms
56,960 KB
testcase_06 WA -
testcase_07 WA -
testcase_08 WA -
testcase_09 WA -
testcase_10 WA -
testcase_11 WA -
testcase_12 AC 46 ms
64,952 KB
testcase_13 AC 49 ms
66,536 KB
testcase_14 WA -
testcase_15 AC 38 ms
56,960 KB
testcase_16 AC 38 ms
56,772 KB
testcase_17 AC 37 ms
55,784 KB
testcase_18 AC 35 ms
56,616 KB
testcase_19 AC 44 ms
56,716 KB
testcase_20 WA -
testcase_21 WA -
testcase_22 WA -
testcase_23 AC 40 ms
55,428 KB
testcase_24 WA -
testcase_25 WA -
testcase_26 WA -
testcase_27 AC 37 ms
55,468 KB
testcase_28 WA -
testcase_29 TLE -
testcase_30 TLE -
testcase_31 TLE -
testcase_32 TLE -
testcase_33 TLE -
testcase_34 WA -
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ソースコード

diff # 

N,P = map(int,input().split())

if N == P:
  print(pow(N,N - 2,P))
  exit()

mod = 998244353
Mod,MOd,MOD = 1045430273,1051721729,1053818881

n = N

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

fact_inv = [1 for i in range(n+1)]
fact_inv[-1] = pow(fact[-1],P-2,P)
for i in range(n,0,-1):
  fact_inv[i-1] = fact_inv[i]*i % P

def binom(n,r):
  res = fact[n] * (fact_inv[n - r] * fact_inv[r] % P) % P
  return res

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 = pow(n,mod - 2,mod)
  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) <= 60:
    return convolute_naive(s,t)
  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):
  assert (f[0] != 0)
  if deg == -1:
    deg = len(f)
  res = [0] * deg
  res[0] = pow(f[0],mod-2,mod)
  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] = pow(i + 1,mod-2,mod) * 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))
  res = fps_integrate(res)
  return res[:deg]

def fps_exp(f,deg = -1):
  assert (f[0] == 0)
  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]

def fps_pow(f,k,deg = -1):
  if deg == -1:
    deg = len(f)
  if k == 0:
    return [1] + [0] * (deg - 1)
  while len(f) < deg:
    f.append(0)
  p = 0
  while p < deg:
    if f[p]:
      break
    p += 1
  if p * k >= deg:
    return [0] * deg
  a = f[p]
  g = [0 for _ in range(deg - p)]
  a_inv = pow(a,mod-2,mod)
  for i in range(deg - p):
    g[i] = f[i + p] * a_inv % mod
  g = fps_log(g)
  for i in range(deg-p):
    g[i] = g[i] * k % mod
  g = fps_exp(g)
  a = pow(a,k,mod)
  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 mod_inv(a,mod):
  if mod == 1:
    return 0
  a %= mod
  b,s,t = mod,1,0
  while True:
    if a == 1:
      return s
    t -= (b // a) * s
    b %= a
    if b == 1:
      return t + mod
    s -= (a // b) * t
    a %= b

def gcd_inv(a,mod):
  a %= mod
  b,s,t = mod,1,0
  while True:
    if a == 0:
      return (b,t + mod)
    t -= (b // a) * s
    b %= a
    if b == 0:
      return (a,s)
    s -= (a // b) * t
    a %= b

# (0,0)のとき存在しない.
def garner(Rem,Mod):
  assert (len(Rem) == len(Mod))

  r,m = 0,1
  for i in range(len(Rem)):
    assert (Mod[i])
    Rem[i] %= Mod[i]
    m1,r1 = Mod[i],Rem[i]
    if m < m1:
      m,m1,r,r1 = m1,m,r1,r
    if m % m1 == 0:
      if r % m1 != r1:
        return (0,0)

    g,im = gcd_inv(m,m1)
    y = abs(r1 - r)
    if y % g:
      return (0,0)
    u1 = m1 // g
    y = y // g % u1
    if (r > r1 and y != 0):
      y = u1 - y
    x = y * im % u1
    r += x * m
    m *= u1
  return (r,m)

# Modの中身が互いに素じゃないとダメ
def Garner(Rem,Mod,mod):
  assert (len(Rem) == len(Mod))

  Rem.append(0)
  Mod.append(mod)
  n = len(Mod)
  coffs = [1] * n
  constants = [0] * n
  for i in range(n - 1):
    v = (Rem[i] - constants[i]) * mod_inv(coffs[i],Mod[i]) % Mod[i]
    for j in range(i + 1,n):
      constants[j] = (constants[j] + coffs[j] * v) % Mod[j]
      coffs[j] = (coffs[j] * Mod[i]) % Mod[j]
  return constants[-1]

f = [1]
for i in range(1,N):
  c = pow(i + 1,i - 1,P) * fact_inv[i] % P
  f.append(c)

ans = 0
g = [0] * N
g[0] = 1
for n in range(1,N + 1):
  res = binom(N,n) * pow(n,n - 2,P) % P
  root,iroot,rate2,irate2,rate3,irate3 = prepared_fft(mod)
  h = convolute(f,g)[:N]
  root,iroot,rate2,irate2,rate3,irate3 = prepared_fft(Mod)
  hh = convolute(f,g)[:N]
  root,iroot,rate2,irate2,rate3,irate3 = prepared_fft(MOd)
  hhh = convolute(f,g)[:N]
  root,iroot,rate2,irate2,rate3,irate3 = prepared_fft(MOD)
  hhhh = convolute(f,g)[:N]
  for i in range(N):
    g[i] = Garner([h[i],hh[i],hhh[i],hhhh[i]],[mod,Mod,MOd,MOD],P)
  res = res * fact[N - n] % P
  res = res * g[N - n] % P
  ans += res
  ans %= P
print(ans)
0