結果
問題 | No.1302 Random Tree Score |
ユーザー |
![]() |
提出日時 | 2024-09-19 21:08:09 |
言語 | PyPy3 (7.3.15) |
結果 |
AC
|
実行時間 | 2,282 ms / 3,000 ms |
コード長 | 1,836 bytes |
コンパイル時間 | 196 ms |
コンパイル使用メモリ | 82,048 KB |
実行使用メモリ | 250,908 KB |
最終ジャッジ日時 | 2024-09-19 21:08:54 |
合計ジャッジ時間 | 39,756 ms |
ジャッジサーバーID (参考情報) |
judge4 / judge1 |
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ファイルパターン | 結果 |
---|---|
sample | AC * 3 |
other | AC * 14 |
ソースコード
mod = 998244353 R = 3 Rinv = 332748118 W = [pow(R, (mod-1)>>i, mod) for i in range(24)] Winv = [pow(Rinv, (mod-1)>>i, mod) for i in range(24)] def fft(k, f): for l in range(k, 0, -1): d = 1<<l-1 U = [1] for i in range(d): U.append(U[-1]*W[l]%mod) for i in range(1<<k-l): for j in range(d): s = i*2*d+j f[s], f[s+d] = (f[s]+f[s+d])%mod, U[j]*(f[s]-f[s+d])%mod def fftinv(k, f): for l in range(1, k+1): d = 1<<l-1 for i in range(1<<k-l): u = 1 for j in range(i*2*d, (i*2+1)*d): f[j+d] *= u f[j], f[j+d] = (f[j]+f[j+d])%mod, (f[j]-f[j+d])%mod u *= Winv[l] u %= mod def convolution(a, b): le = len(a)+len(b)-1 k = le.bit_length() n = 1<<k a = a+[0]*(n-len(a)) b = b+[0]*(n-len(b)) fft(k, a) fft(k, b) for i in range(n): a[i] *= b[i] a[i] %= mod fftinv(k, a) ninv = pow(n, mod-2, mod) for i in range(le): a[i] *= ninv a[i] %= mod return a[:le] def FPSinv(H): I=[pow(H[0],M-2,M)] l=1 while l<len(H): I+=[0]*l nI=convolution(H[:l*2],convolution(I,I)[:l*2])[:l*2] for i in range(l*2): nI[i]=(2*I[i]-nI[i])%M I=nI l*=2 return I[:len(H)] def FPSlog(H): H1=[H[i]*i%M for i in range(1,len(H))]+[0] H2=FPSinv(H) I=convolution(H1,H2) I=[0]+[I[i]*fb[i+1]*fa[i]%M for i in range(len(H)-1)] return I def FPSexp(H): I=[1] l=1 while l<len(H): I+=[0]*l I2=FPSlog(I)[:l*2] I3=H[:l*2] I3[0]+=1 for i in range(l*2): I3[i]-=I2[i] nI=convolution(I,I3)[:l*2] I=nI l*=2 return I[:len(H)] n=int(input()) L=1<<17 M=998244353 fa=[1,1] fb=[1,1] for i in range(2,L+1): fa+=[fa[-1]*i%M] fb+=[fb[-1]*(M//i)*fb[M%i]*fa[M%i-1]*(-1)%M] q1=[(i+1)*fb[i]%M for i in range(L)] q2=FPSlog(q1) for i in range(L): q2[i]*=n q2[i]%=M q3=FPSexp(q2) a=q3[n-2] print(a*fa[n-2]*pow(pow(n,n-2,M),M-2,M)%M)