結果

問題 No.2181 LRM Question 2
ユーザー vwxyz
提出日時 2023-05-19 07:02:51
言語 PyPy3
(7.3.15)
結果
TLE  
実行時間 -
コード長 8,658 bytes
コンパイル時間 318 ms
コンパイル使用メモリ 82,476 KB
実行使用メモリ 140,088 KB
最終ジャッジ日時 2024-12-17 17:05:39
合計ジャッジ時間 17,933 ms
ジャッジサーバーID
（参考情報） 		judge4 / 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 * 2 TLE * 1
other AC * 19 TLE * 4
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

import sys
readline=sys.stdin.readline
import math
from collections import defaultdict
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
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
def CRT(remainder_lst,mod_lst):
    assert len(remainder_lst)==len(mod_lst)
    if not remainder_lst:
        return 0,1
    remainder,mod=remainder_lst[0],mod_lst[0]
    for r,m in zip(remainder_lst[1:],mod_lst[1:]):
        if (r,m)==(-1,0):
            remainder,mod=-1,0
            break
        r%=m
        g=math.gcd(mod,m)
        lcm=LCM(mod,m)
        if remainder%g!=r%g:
            remainder,mod=-1,0
            break
        remainder,mod=(r+m*((remainder-r)//g)*Extended_Euclid(m//g,mod//g)[0])%lcm,lcm
    return remainder,mod
def LCM(n,m):
    if n or m:
        return abs(n)*abs(m)//math.gcd(n,m)
    return 0
class Lucas_Prime:
    def __init__(self,P,e=1):
        self.P=P
        self.e=e
        self.mod=self.P**self.e
        self.factorial=[1]
        for i in range(1,self.mod):
            self.factorial.append(self.factorial[-1])
            if i%P:
                self.factorial[i]*=i
                self.factorial[i]%=self.mod
    
    def Comb(self,N,K,divisible_count=False):
        if K<0 or K>N:
            return 0
        K0,K1=K,N-K
        N_lst=[]
        N_=N
        while N_:
            N_lst.append(N_%self.mod)
            N_//=self.P
        K0_lst=[]
        K0_=K0
        for _ in range(len(N_lst)):
            K0_lst.append(K0_%self.mod)
            K0_//=self.P
        K1_lst=[]
        K1_=K1
        for _ in range(len(N_lst)):
            K1_lst.append(K1_%self.mod)
            K1_//=self.P
        retu,retu_rev=1,1
        for n in N_lst:
            retu*=self.factorial[n]
            retu%=self.mod
        for k0 in K0_lst:
            retu_rev*=self.factorial[k0]
            retu_rev%=self.mod
        for k1 in K1_lst:
            retu_rev*=self.factorial[k1]
            retu_rev%=self.mod
        retu*=MOD(self.mod).Pow(retu_rev,-1)
        if self.P!=2 or self.e<=2:
            cnt=0
            N_=N//self.mod
            K0_=K0//self.mod
            K1_=K1//self.mod
            while N_:
                cnt+=N_
                N_//=self.P
            while K0_:
                cnt+=K0_
                K0_//=self.P
            while K1_:
                cnt+=K1_
                K1_//=self.P
            if cnt%2==1:
                retu*=-1
        retu%=self.mod
        div_cnt=0
        N_,K0_,K1_=N,K0,K1
        while N_:
            div_cnt+=N_
            N_//=self.P
        while K0_:
            div_cnt-=K0_
            K0_//=self.P
        while K1_:
            div_cnt-=K1_
            K1_//=self.P
        if divisible_count:
            return retu,div_cnt
        else:
            retu*=pow(self.P,div_cnt,self.mod)
            retu%=self.mod
            return retu
class Lucas:
    def __init__(self,mod):
        self.mod=mod
        P=Prime(int(self.mod**.5))
        self.LP=[(p,e,Lucas_Prime(p,e)) for p,e in P.Factorize(mod).items()]
    def Comb(self,N,K):
        lst_r=[]
        lst_m=[]
        for p,e,lp in self.LP:
            lst_r.append(lp.Comb(N,K))
            lst_m.append(p**e)
        r,_=CRT(lst_r,lst_m)
        return r
def Factorize(N):
    assert N>=1
    factors=defaultdict(int)
    for p in range(2,N):
        if p**2>N:
            break
        while N%p==0:
            factors[p]+=1
            N//=p
    if N!=1:
        factors[N]+=1
    return factors
L,R,M=map(int,readline().split())
rem_lst,mod_lst=[],[]
for p,e in Factorize(M).items():
    LP=Lucas_Prime(p,e)
    ans=0
    mod=p**e
    for m in range(L,R+1):
        ans+=LP.Comb(2*m,m)-2
        ans%=mod
    rem_lst.append(ans)
    mod_lst.append(mod)
ans,_=CRT(rem_lst,mod_lst)
print(ans)
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