結果
| 問題 |
No.2582 Random Average^K
|
| コンテスト | |
| ユーザー |
 とりゐ
|
| 提出日時 | 2023-06-08 01:49:46 |
| 言語 | PyPy3 (7.3.15) |
| 結果 |
TLE
|
| 実行時間 | - |
| コード長 | 5,815 bytes |
| コンパイル時間 | 323 ms |
| コンパイル使用メモリ | 82,280 KB |
| 実行使用メモリ | 113,196 KB |
| 最終ジャッジ日時 | 2024-09-27 03:48:21 |
| 合計ジャッジ時間 | 4,492 ms |
|
ジャッジサーバーID （参考情報） |
judge3 / judge2 |
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| ファイルパターン | 結果 |
|---|---|
| sample | AC * 3 |
| other | AC * 3 TLE * 1 -- * 11 |
ソースコード
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]
mod=998244353
table_size=2*10**5
fac=[1]*(table_size+1)
finv=[1]*(table_size+1)
for i in range(2,table_size+1):
fac[i]=fac[i-1]*i%mod
finv[table_size]=pow(fac[table_size],mod-2,mod)
for i in range(table_size-1,-1,-1):
finv[i]=finv[i+1]*(i+1)%mod
def rebuild(n):
global table_size,fac,finv
fac+=[0]*(n-table_size)
fac+=[0]*(n-table_size)
finv+=[0]*(n-table_size)
for i in range(table_size+1,n+1):
fac[i]=fac[i-1]*i%mod
finv[n]=inv(fac[n])
for i in range(n-1,table_size,-1):
finv[i]=finv[i+1]*(i+1)%mod
table_size=n
def binom(n,k):
if n<0 or k<0:
return 0
if k>n:
return 0
if n>table_size:
rebuild(n+10**4)
return (fac[n]*finv[k]%mod)*finv[n-k]%mod
def fpow(x,k):
res=1
while k:
if k&1:
res=res*x%mod
x=x*x%mod
k>>=1
return res
def inv(a):
if a<table_size:
return fac[a-1]*finv[a]%mod
return fpow(a,mod-2)
def integral(a):
n=len(a)
b=[0]*(n+1)
for i in range(n):
b[i+1]=a[i]*inv(i+1)%mod
return b
N,K=map(int,input().split())
ans=0
for k in range(N+1):
a=[0]*N
sgn=1
for i in range(k+1):
tmp=1
for j in range(N):
a[N-1-j]+=sgn*binom(N,i)*binom(N-1,j)%mod*tmp
a[N-1-j]%=mod
tmp*=k-i
tmp%=mod
sgn=-sgn
b=[0]*(K+1)
tmp=1
for i in range(K+1):
b[K-i]=binom(K,i)*tmp%mod
tmp*=k
tmp%=mod
c=multiply(a,b)
ans+=sum(integral(c))
ans%=mod
ans*=finv[N-1]
ans%=mod
ans*=pow(N,K*(mod-2),mod)
print(ans%mod)
exit()
def modint_to_frac(a,mod):
a%=mod
if a==0:
return '0/1'
for X in range(1,10000):
Y=a*X%mod
if 0<Y<10000:
return str(Y)+'/'+str(X)
if mod-10000<Y<mod:
return '-'+str(mod-Y)+'/'+str(X)
return 'inexpressible'
print(modint_to_frac(ans,mod))