結果

問題 No.1887 K Consecutive Ks (Easy)
ユーザー miscalc
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
このコードへのチャレンジ
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ファイルパターン 結果
sample AC * 3
other AC * 16
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ソースコード

diff #
プレゼンテーションモードにする

# ACL-for-python by shakayami
# https://github.com/shakayami/ACL-for-python/blob/master/convolution.py
class FFT():
def primitive_root_constexpr(self,m):
if m==2:return 1
if m==167772161:return 3
if m==469762049:return 3
if m==754974721:return 11
if m==998244353:return 3
divs=[0]*20
divs[0]=2
cnt=1
x=(m-1)//2
while(x%2==0):x//=2
i=3
while(i*i<=x):
if (x%i==0):
divs[cnt]=i
cnt+=1
while(x%i==0):
x//=i
i+=2
if x>1:
divs[cnt]=x
cnt+=1
g=2
while(1):
ok=True
for i in range(cnt):
if pow(g,(m-1)//divs[i],m)==1:
ok=False
break
if ok:
return g
g+=1
def bsf(self,x):
res=0
while(x%2==0):
res+=1
x//=2
return res
butterfly_first=True
butterfly_inv_first=True
sum_e=[0]*30
sum_ie=[0]*30
def __init__(self,MOD):
self.mod=MOD
self.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=False
es=[0]*30
ies=[0]*30
cnt2=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]=e
ies[i-2]=ie
e=(e*e)%self.mod
ie=(ie*ie)%self.mod
now=1
for i in range(cnt2-2):
self.sum_e[i]=((es[i]*now)%self.mod)
now*=ies[i]
now%=self.mod
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
r%=self.mod
a[i+offset]=l+r
a[i+offset]%=self.mod
a[i+offset+p]=l-r
a[i+offset+p]%=self.mod
now*=self.sum_e[(~s & -~s).bit_length()-1]
now%=self.mod
def butterfly_inv(self,a):
n=len(a)
h=(n-1).bit_length()
if self.butterfly_inv_first:
self.butterfly_inv_first=False
es=[0]*30
ies=[0]*30
cnt2=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]=e
ies[i-2]=ie
e=(e*e)%self.mod
ie=(ie*ie)%self.mod
now=1
for i in range(cnt2-2):
self.sum_ie[i]=((ies[i]*now)%self.mod)
now*=es[i]
now%=self.mod
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
a[i+offset]%=self.mod
a[i+offset+p]=(l-r)*inow
a[i+offset+p]%=self.mod
inow*=self.sum_ie[(~s & -~s).bit_length()-1]
inow%=self.mod
def 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,n
a,b=b,a
res=[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.mod
return res
z=1<<((n+m-2).bit_length())
a=a+[0]*(z-n)
b=b+[0]*(z-m)
self.butterfly(a)
self.butterfly(b)
c=[0]*z
for i in range(z):
c[i]=(a[i]*b[i])%self.mod
self.butterfly_inv(c)
iz=pow(z,self.mod-2,self.mod)
for i in range(n+m-1):
c[i]=(c[i]*iz)%self.mod
return c[:n+m-1]
mod = 998244353
CONV = FFT(mod)
n, m = map(int, input().split())
d = [0] * (n + 10)
for i in range(2, m + 1):
k = 1
while k * i <= n:
d[k * i - 1] += 1
k += 1
pw = [0] * (n + 10)
pw[1], pw[2] = 1, m - 2
for i in range(2, n):
pw[i + 1] = (m - 1) * pw[i] % mod
dp1 = [0] * (n + 10)
dp2 = [1] * (n + 10)
for i in range(n):
dp2[i + 1] = (m - 1) * dp2[i] % mod
def onlineconvolution(l, r):
if l + 1 == r:
return
c = (l + r) // 2
onlineconvolution(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] -= mod
dp10 = 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] -= mod
onlineconvolution(c, r)
onlineconvolution(0, n + 1)
ans = pow(m, n, mod) + mod - dp2[n]
if ans >= mod:
ans -= mod
print(ans)
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