結果
問題 | No.890 移調の限られた旋法 |
ユーザー | vwxyz |
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 |
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テストケース
テストケース表示入力 | 結果 | 実行時間 実行使用メモリ |
---|---|---|
testcase_00 | AC | 42 ms
53,888 KB |
testcase_01 | AC | 40 ms
53,888 KB |
testcase_02 | AC | 38 ms
53,504 KB |
testcase_03 | AC | 39 ms
53,632 KB |
testcase_04 | AC | 39 ms
53,504 KB |
testcase_05 | AC | 39 ms
53,632 KB |
testcase_06 | AC | 39 ms
53,376 KB |
testcase_07 | AC | 38 ms
53,888 KB |
testcase_08 | AC | 39 ms
53,632 KB |
testcase_09 | AC | 43 ms
53,760 KB |
testcase_10 | AC | 40 ms
53,888 KB |
testcase_11 | AC | 39 ms
53,760 KB |
testcase_12 | AC | 39 ms
53,632 KB |
testcase_13 | AC | 452 ms
172,544 KB |
testcase_14 | AC | 427 ms
172,288 KB |
testcase_15 | AC | 429 ms
172,288 KB |
testcase_16 | AC | 452 ms
172,160 KB |
testcase_17 | AC | 395 ms
162,944 KB |
testcase_18 | AC | 420 ms
163,316 KB |
testcase_19 | AC | 252 ms
134,784 KB |
testcase_20 | AC | 203 ms
112,512 KB |
testcase_21 | AC | 84 ms
77,568 KB |
testcase_22 | AC | 361 ms
159,744 KB |
testcase_23 | AC | 425 ms
163,840 KB |
testcase_24 | AC | 273 ms
135,296 KB |
testcase_25 | AC | 106 ms
83,456 KB |
testcase_26 | AC | 418 ms
163,968 KB |
testcase_27 | AC | 438 ms
164,352 KB |
testcase_28 | AC | 312 ms
147,712 KB |
testcase_29 | AC | 225 ms
123,392 KB |
testcase_30 | AC | 392 ms
163,468 KB |
testcase_31 | AC | 273 ms
134,016 KB |
testcase_32 | AC | 390 ms
161,956 KB |
testcase_33 | AC | 410 ms
162,944 KB |
testcase_34 | AC | 408 ms
162,816 KB |
ソースコード
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)