結果

問題 No.890 移調の限られた旋法
ユーザー vwxyzvwxyz
提出日時 2024-04-10 08:56:33
言語 PyPy3
(7.3.15)
結果
AC  
実行時間 452 ms / 2,000 ms
コード長 5,308 bytes
コンパイル時間 216 ms
コンパイル使用メモリ 82,360 KB
実行使用メモリ 172,544 KB
最終ジャッジ日時 2024-10-02 10:41:05
合計ジャッジ時間 9,318 ms
ジャッジサーバーID
(参考情報)
judge1 / judge5
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 * 32
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 #
プレゼンテーションモードにする

def Extended_Euclid(n,m):
stack=[]
while m:
stack.append((n,m))
n,m=m,n%m
if n>=0:
x,y=1,0
else:
x,y=-1,0
for i in range(len(stack)-1,-1,-1):
n,m=stack[i]
x,y=y,x-(n//m)*y
return x,y
class MOD:
def __init__(self,p,e=None):
self.p=p
self.e=e
if self.e==None:
self.mod=self.p
else:
self.mod=self.p**self.e
def Pow(self,a,n):
a%=self.mod
if n>=0:
return pow(a,n,self.mod)
else:
#assert math.gcd(a,self.mod)==1
x=Extended_Euclid(a,self.mod)[0]
return pow(x,-n,self.mod)
def Build_Fact(self,N):
assert N>=0
self.factorial=[1]
if self.e==None:
for i in range(1,N+1):
self.factorial.append(self.factorial[-1]*i%self.mod)
else:
self.cnt=[0]*(N+1)
for i in range(1,N+1):
self.cnt[i]=self.cnt[i-1]
ii=i
while ii%self.p==0:
ii//=self.p
self.cnt[i]+=1
self.factorial.append(self.factorial[-1]*ii%self.mod)
self.factorial_inve=[None]*(N+1)
self.factorial_inve[-1]=self.Pow(self.factorial[-1],-1)
for i in range(N-1,-1,-1):
ii=i+1
while ii%self.p==0:
ii//=self.p
self.factorial_inve[i]=(self.factorial_inve[i+1]*ii)%self.mod
def Build_Inverse(self,N):
self.inverse=[None]*(N+1)
assert self.p>N
self.inverse[1]=1
for n in range(2,N+1):
if n%self.p==0:
continue
a,b=divmod(self.mod,n)
self.inverse[n]=(-a*self.inverse[b])%self.mod
def Inverse(self,n):
return self.inverse[n]
def Fact(self,N):
if N<0:
return 0
retu=self.factorial[N]
if self.e!=None and self.cnt[N]:
retu*=pow(self.p,self.cnt[N],self.mod)%self.mod
retu%=self.mod
return retu
def Fact_Inve(self,N):
if self.e!=None and self.cnt[N]:
return None
return self.factorial_inve[N]
def Comb(self,N,K,divisible_count=False):
if K<0 or K>N:
return 0
retu=self.factorial[N]*self.factorial_inve[K]%self.mod*self.factorial_inve[N-K]%self.mod
if self.e!=None:
cnt=self.cnt[N]-self.cnt[N-K]-self.cnt[K]
if divisible_count:
return retu,cnt
else:
retu*=pow(self.p,cnt,self.mod)
retu%=self.mod
return retu
import math
class Prime:
def __init__(self,N):
assert N<=10**8
self.smallest_prime_factor=[None]*(N+1)
for i in range(2,N+1,2):
self.smallest_prime_factor[i]=2
n=int(N**.5)+1
for p in range(3,n,2):
if self.smallest_prime_factor[p]==None:
self.smallest_prime_factor[p]=p
for i in range(p**2,N+1,2*p):
if self.smallest_prime_factor[i]==None:
self.smallest_prime_factor[i]=p
for p in range(n,N+1):
if self.smallest_prime_factor[p]==None:
self.smallest_prime_factor[p]=p
self.primes=[p for p in range(N+1) if p==self.smallest_prime_factor[p]]
def Factorize(self,N):
assert N>=1
factors=defaultdict(int)
if N<=len(self.smallest_prime_factor)-1:
while N!=1:
factors[self.smallest_prime_factor[N]]+=1
N//=self.smallest_prime_factor[N]
else:
for p in self.primes:
while N%p==0:
N//=p
factors[p]+=1
if N<p*p:
if N!=1:
factors[N]+=1
break
if N<=len(self.smallest_prime_factor)-1:
while N!=1:
factors[self.smallest_prime_factor[N]]+=1
N//=self.smallest_prime_factor[N]
break
else:
if N!=1:
factors[N]+=1
return factors
def Divisors(self,N):
assert N>0
divisors=[1]
for p,e in self.Factorize(N).items():
pow_p=[1]
for _ in range(e):
pow_p.append(pow_p[-1]*p)
divisors=[i*j for i in divisors for j in pow_p]
return divisors
def Is_Prime(self,N):
return N==self.smallest_prime_factor[N]
def Totient(self,N):
for p in self.Factorize(N).keys():
N*=p-1
N//=p
return N
def Mebius(self,N):
fact=self.Factorize(N)
for e in fact.values():
if e>=2:
return 0
else:
if len(fact)%2==0:
return 1
else:
return -1
N,K=map(int,input().split())
mod=10**9+7
MD=MOD(mod)
MD.Build_Fact(N)
cnt=[0]*(N+1)
for i in range(1,N+1):
g=math.gcd(N,i)
n=N//g
if K%n==0:
cnt[i]=MD.Comb(g,K//n)
Pr=Prime(N)
for p in Pr.primes:
for i in range(N//p,0,-1):
cnt[i*p]-=cnt[i]
cnt[i*p]%=mod
ans=sum(cnt[:N])%mod
print(ans)
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