結果
問題 | No.1887 K Consecutive Ks (Easy) |
ユーザー |
![]() |
提出日時 | 2022-03-06 17:30:55 |
言語 | PyPy3 (7.3.15) |
結果 |
AC
|
実行時間 | 259 ms / 2,000 ms |
コード長 | 5,323 bytes |
コンパイル時間 | 395 ms |
コンパイル使用メモリ | 81,792 KB |
実行使用メモリ | 78,288 KB |
最終ジャッジ日時 | 2024-07-21 03:18:43 |
合計ジャッジ時間 | 3,884 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 * 16 |
ソースコード
# ACL-for-python by shakayami# https://github.com/shakayami/ACL-for-python/blob/master/convolution.pyclass FFT():def primitive_root_constexpr(self,m):if m==2:return 1if m==167772161:return 3if m==469762049:return 3if m==754974721:return 11if m==998244353:return 3divs=[0]*20divs[0]=2cnt=1x=(m-1)//2while(x%2==0):x//=2i=3while(i*i<=x):if (x%i==0):divs[cnt]=icnt+=1while(x%i==0):x//=ii+=2if x>1:divs[cnt]=xcnt+=1g=2while(1):ok=Truefor i in range(cnt):if pow(g,(m-1)//divs[i],m)==1:ok=Falsebreakif ok:return gg+=1def bsf(self,x):res=0while(x%2==0):res+=1x//=2return resbutterfly_first=Truebutterfly_inv_first=Truesum_e=[0]*30sum_ie=[0]*30def __init__(self,MOD):self.mod=MODself.g=self.primitive_root_constexpr(self.mod)def butterfly(self,a):n=len(a)h=(n-1).bit_length()if self.butterfly_first:self.butterfly_first=Falsees=[0]*30ies=[0]*30cnt2=self.bsf(self.mod-1)e=pow(self.g,(self.mod-1)>>cnt2,self.mod)ie=pow(e,self.mod-2,self.mod)for i in range(cnt2,1,-1):es[i-2]=eies[i-2]=iee=(e*e)%self.modie=(ie*ie)%self.modnow=1for i in range(cnt2-2):self.sum_e[i]=((es[i]*now)%self.mod)now*=ies[i]now%=self.modfor ph in range(1,h+1):w=1<<(ph-1)p=1<<(h-ph)now=1for s in range(w):offset=s<<(h-ph+1)for i in range(p):l=a[i+offset]r=a[i+offset+p]*nowr%=self.moda[i+offset]=l+ra[i+offset]%=self.moda[i+offset+p]=l-ra[i+offset+p]%=self.modnow*=self.sum_e[(~s & -~s).bit_length()-1]now%=self.moddef butterfly_inv(self,a):n=len(a)h=(n-1).bit_length()if self.butterfly_inv_first:self.butterfly_inv_first=Falsees=[0]*30ies=[0]*30cnt2=self.bsf(self.mod-1)e=pow(self.g,(self.mod-1)>>cnt2,self.mod)ie=pow(e,self.mod-2,self.mod)for i in range(cnt2,1,-1):es[i-2]=eies[i-2]=iee=(e*e)%self.modie=(ie*ie)%self.modnow=1for i in range(cnt2-2):self.sum_ie[i]=((ies[i]*now)%self.mod)now*=es[i]now%=self.modfor ph in range(h,0,-1):w=1<<(ph-1)p=1<<(h-ph)inow=1for 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+ra[i+offset]%=self.moda[i+offset+p]=(l-r)*inowa[i+offset+p]%=self.modinow*=self.sum_ie[(~s & -~s).bit_length()-1]inow%=self.moddef convolution(self,a,b):n=len(a);m=len(b)if not(a) or not(b):return []if min(n,m)<=40:if n<m:n,m=m,na,b=b,ares=[0]*(n+m-1)for i in range(n):for j in range(m):res[i+j]+=a[i]*b[j]res[i+j]%=self.modreturn resz=1<<((n+m-2).bit_length())a=a+[0]*(z-n)b=b+[0]*(z-m)self.butterfly(a)self.butterfly(b)c=[0]*zfor i in range(z):c[i]=(a[i]*b[i])%self.modself.butterfly_inv(c)iz=pow(z,self.mod-2,self.mod)for i in range(n+m-1):c[i]=(c[i]*iz)%self.modreturn c[:n+m-1]mod = 998244353CONV = FFT(mod)n, m = map(int, input().split())d = [0] * (n + 10)for i in range(2, m + 1):k = 1while k * i <= n:d[k * i - 1] += 1k += 1pw = [0] * (n + 10)pw[1], pw[2] = 1, m - 2for i in range(2, n):pw[i + 1] = (m - 1) * pw[i] % moddp1 = [0] * (n + 10)dp2 = [1] * (n + 10)for i in range(n):dp2[i + 1] = (m - 1) * dp2[i] % moddef onlineconvolution(l, r):if l + 1 == r:returnc = (l + r) // 2onlineconvolution(l, c)dp20 = dp2[l : c]d0 = d[: r - l]r1 = CONV.convolution(dp20, d0)for i in range(c, r):dp1[i] += r1[i - l]if dp1[i] >= mod:dp1[i] -= moddp10 = dp1[l : c]pw0 = pw[: r - l]r2 = CONV.convolution(dp10, pw0)for i in range(c, r):dp2[i] += mod - r2[i - l]if dp2[i] >= mod:dp2[i] -= modonlineconvolution(c, r)onlineconvolution(0, n + 1)ans = pow(m, n, mod) + mod - dp2[n]if ans >= mod:ans -= modprint(ans)