結果

問題 No.2097 AND^k
ユーザー taiga0629kyoprotaiga0629kyopro
提出日時 2022-09-20 11:02:28
言語 PyPy3
(7.3.15)
結果
AC  
実行時間 2,021 ms / 5,000 ms
コード長 6,662 bytes
コンパイル時間 308 ms
コンパイル使用メモリ 82,416 KB
実行使用メモリ 249,996 KB
最終ジャッジ日時 2024-06-01 17:35:47
合計ジャッジ時間 25,067 ms
ジャッジサーバーID
（参考情報） 		judge5 / judge4
このコードへのチャレンジ
（要ログイン）

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 52 ms
65,196 KB
testcase_01 AC 52 ms
65,240 KB
testcase_02 AC 52 ms
65,156 KB
testcase_03 AC 54 ms
67,256 KB
testcase_04 AC 76 ms
76,532 KB
testcase_05 AC 56 ms
67,100 KB
testcase_06 AC 55 ms
66,224 KB
testcase_07 AC 60 ms
67,792 KB
testcase_08 AC 780 ms
163,580 KB
testcase_09 AC 457 ms
128,344 KB
testcase_10 AC 801 ms
164,128 KB
testcase_11 AC 434 ms
121,668 KB
testcase_12 AC 404 ms
118,464 KB
testcase_13 AC 1,664 ms
249,996 KB
testcase_14 AC 1,629 ms
249,624 KB
testcase_15 AC 1,818 ms
249,632 KB
testcase_16 AC 1,408 ms
235,840 KB
testcase_17 AC 1,766 ms
249,492 KB
testcase_18 AC 1,576 ms
248,660 KB
testcase_19 AC 1,484 ms
242,936 KB
testcase_20 AC 1,445 ms
235,812 KB
testcase_21 AC 1,418 ms
235,816 KB
testcase_22 AC 1,540 ms
248,568 KB
testcase_23 AC 1,479 ms
242,620 KB
testcase_24 AC 52 ms
65,236 KB
testcase_25 AC 2,021 ms
249,472 KB
権限があれば一括ダウンロードができます

ソースコード

diff # 





mod=998244353
#############################
#############
cnb_max=3*10**5
#############

kai=[1]*(cnb_max+1)
rkai=[1]*(cnb_max+1)
for i in range(cnb_max):
    kai[i+1]=kai[i]*(i+1)%mod

rkai[cnb_max]=pow(kai[cnb_max],mod-2,mod)
for i in range(cnb_max):
    rkai[cnb_max-1-i]=rkai[cnb_max-i]*(cnb_max-i)%mod

def cnb(x,y):
    if y>x:
        return 0
    if x<0:return 0
    if y<0:return 0
    return (kai[x]*rkai[y]%mod)*rkai[x-y]%mod


def inv(n):
    return kai[n-1]*rkai[n]%mod

##################################


# AtCoder Libary v1.4 を python に移植したもの
# https://github.com/atcoder/ac-library/blob/master/atcoder/convolution.hpp
#https://judge.yosupo.jp/submission/55648

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]






def naive(n,m,l):
    dp=[0]*(2**m)
    dp[2**m-1]=1
    for i in range(n):
        newdp=[0]*(2**m)
        for j in range(2**m):
            for ai in range(2**m):
                dp[j]%=mod
                newdp[j&ai]+=dp[j]
        dp=newdp[:]
    ans=[0]
    for k in range(1,l+1):
        res=0
        for j in range(2**m):
            res+=pow(j,k,mod)*dp[j]
            res%=mod
        ans.append(res%mod)
    return ans
def sol1(n,m,l):
    fx=[0]*(l+1)
    fx[0]=1
    invn2=pow(2,n*(mod-2),mod)
    for i in range(m):
        gx=[0]*(l+1)
        gx[0]=1
        i2=pow(2,i,mod)
        nod=i2
        for a in range(1,l+1):
            gx[a]=nod*rkai[a]%mod
            gx[a]*=invn2
            gx[a]%=mod
            nod=nod*i2%mod
        fx=multiply(fx,gx)[:l+1]
    ans=[0]
    for k in range(1,l+1):
        res=pow(2,n*m,mod)*kai[k]%mod
        res*=fx[k]
        ans.append(res%mod)
    return ans


def sol2(n,m,l):
    invn2 = pow(2, n * (mod - 2), mod)
    def f(i):
        gx=[0]*(l+1)
        gx[0]=1
        i2 = pow(2, i, mod)
        nod = i2
        for a in range(1, l + 1):
            gx[a] = nod * rkai[a] % mod
            gx[a] *= invn2
            gx[a] %= mod
            nod = nod * i2 % mod
        return gx
    def F(i):
        if i==0:return f(i)
        num=i+1
        if num%2==0:
            res=F(i//2)
            res2=res[:]
            d=pow(2,num//2,mod)
            nod=d
            for a in range(1,l+1):
                res[a]=res[a]*nod%mod
                nod=nod*d%mod
            return multiply(res,res2)[:l+1]
        else:
            return multiply(F(i-1),f(i))[:l+1]
    fx=F(m-1)
    ans = [0]
    for k in range(1, l + 1):
        res = pow(2, n * m, mod) * kai[k] % mod
        res *= fx[k]
        ans.append(res % mod)
    return ans

n,m,l=map(int,input().split())
ans=sol2(n,m,l)
for k in range(1,l+1):print(ans[k])
0