結果

問題 No.1387 Mitarushi's Remodeling
ユーザー googol_S0googol_S0
提出日時 2021-02-07 22:27:58
言語 PyPy3
(7.3.15)
結果
AC  
実行時間 1,358 ms / 2,000 ms
コード長 3,234 bytes
コンパイル時間 1,089 ms
コンパイル使用メモリ 81,920 KB
実行使用メモリ 268,484 KB
最終ジャッジ日時 2024-07-02 15:32:27
合計ジャッジ時間 84,229 ms
ジャッジサーバーID
（参考情報） 		judge2 / judge5
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ファイルパターン 結果
sample AC * 3
other AC * 67
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 # 

_fft_mod = 998244353
_fft_sum_e = [911660635, 509520358, 369330050, 332049552, 983190778, 123842337, 238493703, 975955924, 603855026, 856644456, 131300601,
              842657263, 730768835, 942482514, 806263778, 151565301, 510815449, 503497456, 743006876, 741047443, 56250497, 0, 0, 0, 0, 0, 0, 0, 0, 0]
_fft_sum_ie = [86583718, 372528824, 373294451, 645684063, 112220581, 692852209, 155456985, 797128860, 90816748, 860285882, 927414960,
               354738543, 109331171, 293255632, 535113200, 308540755, 121186627, 608385704, 438932459, 359477183, 824071951, 0, 0, 0, 0, 0, 0, 0, 0, 0]
 
 
def butterfly_998244353(a):
    n = len(a)
    h = (n - 1).bit_length()
    for ph in range(1, h + 1):
        w = 1 << (ph - 1)
        p = 1 << (h - ph)
        now = 1
        for s in range(w):
            offset = s << (h - ph + 1)
            for i in range(p):
                l = a[i + offset]
                r = a[i + offset + p] * now % _fft_mod
                a[i + offset] = (l + r) % _fft_mod
                a[i + offset + p] = (l - r) % _fft_mod
            now = now * _fft_sum_e[(~s & -~s).bit_length() - 1] % _fft_mod
 
 
def butterfly_inv_998244353(a):
    n = len(a)
    h = (n - 1).bit_length()
    for ph in range(h, 0, -1):
        w = 1 << (ph - 1)
        p = 1 << (h - ph)
        inow = 1
        for s in range(w):
            offset = s << (h - ph + 1)
            for i in range(p):
                l = a[i + offset]
                r = a[i + offset + p]
                a[i + offset] = (l + r) % _fft_mod
                a[i + offset + p] = (l - r) * inow % _fft_mod
            inow = inow * _fft_sum_ie[(~s & -~s).bit_length() - 1] % _fft_mod
 
 
def convolution_998244353(a, b):
    a = a.copy()
    b = b.copy()
    n = len(a)
    m = len(b)
    if n == 0 or m == 0:
        return []
    if min(n, m) <= 60:
        if n < m:
            n, m = m, n
            a, b = b, a
        ans = [0] * (n + m - 1)
        for i in range(n):
            for j in range(m):
                ans[i + j] = (ans[i + j] + a[i] * b[j] % _fft_mod) % _fft_mod
        return ans
 
    z = 1 << (n + m - 2).bit_length()
    a += [0] * (z - n)
    b += [0] * (z - m)
    butterfly_998244353(a)
    butterfly_998244353(b)
    for i in range(z):
        a[i] = a[i] * b[i] % _fft_mod
    butterfly_inv_998244353(a)
    a = a[:n + m - 1]
    iz = pow(z, _fft_mod - 2, _fft_mod)
    for i in range(n + m - 1):
        a[i] = a[i] * iz % _fft_mod
    
    return a

mod=998244353
def cmb(n,r):
  if r<0 or r>n:
    return 0
  return (g1[n]*g2[r]*g2[n-r])%mod

g1=[1,1]
g2=[1,1]
inv=[0,1]
for i in range(2,1000003):
  g1.append((g1[-1]*i)%mod)
  inv.append((-inv[mod%i]*(mod//i))%mod)
  g2.append((g2[-1]*inv[-1])%mod)
g2.append(1)
G=[1,1]
for i in range(1,1000003):
  G.append((G[-1]*i+1)%mod)
def psum(N,K):
  if N<K:
    K=N
  return (g1[N]*G[N-K]*(K-N)*g2[N-K]+G[N+1]-1)%mod

def solve(A,N,K):
  P=0
  B=convolution_998244353(A[:], A[::-1])
  for i in range(N-1):
    P+=B[i]*(psum(N-1,K)-psum(N-1-abs(N-1-i),K))
  return P%mod

N,K=map(int,input().split())
M=list(map(int,input().split()))
X=1
for i in range(N):
  X=X*M[i]%mod
inv=pow(2,mod-2,mod)
A=[(M[i]+1)*inv%mod for i in range(N)]
ANS=solve(A,N,K)
print(ANS*X%mod)
0