結果
問題 | No.886 Direct |
ユーザー | vwxyz |
提出日時 | 2021-09-30 09:51:42 |
言語 | PyPy3 (7.3.15) |
結果 |
AC
|
実行時間 | 3,697 ms / 4,000 ms |
コード長 | 4,749 bytes |
コンパイル時間 | 247 ms |
コンパイル使用メモリ | 82,428 KB |
実行使用メモリ | 296,728 KB |
最終ジャッジ日時 | 2024-07-17 13:10:03 |
合計ジャッジ時間 | 40,310 ms |
ジャッジサーバーID (参考情報) |
judge5 / judge3 |
(要ログイン)
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 | 43 ms
56,692 KB |
testcase_01 | AC | 43 ms
55,920 KB |
testcase_02 | AC | 44 ms
57,036 KB |
testcase_03 | AC | 200 ms
81,224 KB |
testcase_04 | AC | 44 ms
57,152 KB |
testcase_05 | AC | 43 ms
55,780 KB |
testcase_06 | AC | 43 ms
55,768 KB |
testcase_07 | AC | 44 ms
55,712 KB |
testcase_08 | AC | 43 ms
55,740 KB |
testcase_09 | AC | 43 ms
55,524 KB |
testcase_10 | AC | 44 ms
56,488 KB |
testcase_11 | AC | 44 ms
55,160 KB |
testcase_12 | AC | 43 ms
56,728 KB |
testcase_13 | AC | 43 ms
55,876 KB |
testcase_14 | AC | 43 ms
55,684 KB |
testcase_15 | AC | 44 ms
56,816 KB |
testcase_16 | AC | 43 ms
55,440 KB |
testcase_17 | AC | 187 ms
80,236 KB |
testcase_18 | AC | 237 ms
82,008 KB |
testcase_19 | AC | 234 ms
81,720 KB |
testcase_20 | AC | 183 ms
80,488 KB |
testcase_21 | AC | 210 ms
81,316 KB |
testcase_22 | AC | 233 ms
83,052 KB |
testcase_23 | AC | 1,622 ms
229,332 KB |
testcase_24 | AC | 1,851 ms
233,044 KB |
testcase_25 | AC | 1,188 ms
177,708 KB |
testcase_26 | AC | 1,452 ms
212,964 KB |
testcase_27 | AC | 3,211 ms
265,744 KB |
testcase_28 | AC | 3,129 ms
258,884 KB |
testcase_29 | AC | 3,045 ms
294,904 KB |
testcase_30 | AC | 3,036 ms
294,940 KB |
testcase_31 | AC | 3,697 ms
296,160 KB |
testcase_32 | AC | 3,651 ms
296,548 KB |
testcase_33 | AC | 3,652 ms
296,728 KB |
testcase_34 | AC | 3,687 ms
295,072 KB |
testcase_35 | AC | 3,687 ms
295,744 KB |
ソースコード
import math from collections import defaultdict 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 factorize=defaultdict(int) if N<=len(self.smallest_prime_factor)-1: while N!=1: factorize[self.smallest_prime_factor[N]]+=1 N//=self.smallest_prime_factor[N] else: for p in self.primes: while N%p==0: N//=p factorize[p]+=1 if N<p*p: if N!=1: factorize[N]+=1 break if N<=len(self.smallest_prime_factor)-1: while N!=1: factorize[self.smallest_prime_factor[N]]+=1 N//=self.smallest_prime_factor[N] break else: if N!=1: factorize[N]+=1 return factorize def Divisors(self,N): assert N>0 divisors=[1] for p,e in self.Factorize(N).items(): A=[1] for _ in range(e): A.append(A[-1]*p) divisors=[i*j for i in divisors for j in A] 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 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=1): self.p=p self.e=e 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] self.cnt=[0]*(N+1) for i in range(1,N+1): ii=i self.cnt[i]=self.cnt[i-1] 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 Fact(self,N): if N<0: return 0 return self.factorial[N]*pow(self.p,self.cnt[N],self.mod)%self.mod def Fact_Inve(self,N): if 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.factorial_inve[N-K]%self.mod 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 H,W=map(int,input().split()) cnt=[0]*(max(H,W)+1) mod=10**9+7 MD=MOD(mod) MD.Build_Fact(max(H,W)+1) P=Prime(max(H,W)+1) for g in range(1,max(H,W)+1): n_H,c_H=divmod(H,g) n_W,c_W=divmod(W,g) cnt[g]=((MD.Comb(n_H,2)*(g-c_H)+MD.Comb(n_H+1,2)*c_H)*(MD.Comb(n_W,2)*(g-c_W)+MD.Comb(n_W+1,2)*c_W)*2%mod) cnt[g]+=H*(MD.Comb(n_W,2)*(g-c_W)+MD.Comb(n_W+1,2)*c_W)+W*(MD.Comb(n_H,2)*(g-c_H)+MD.Comb(n_H+1,2)*c_H) ans=0 for g in range(1,max(H,W)+1): ans+=P.Mebius(g)*cnt[g] ans%=mod print(ans)