結果

問題 No.665 Bernoulli Bernoulli
コンテスト
ユーザー vwxyz
提出日時 2021-08-27 17:11:35
言語 Python3
(3.13.1 + numpy 2.2.1 + scipy 1.14.1)
結果
TLE  
実行時間 -
コード長 4,535 bytes
コンパイル時間 258 ms
コンパイル使用メモリ 13,184 KB
実行使用メモリ 24,704 KB
最終ジャッジ日時 2024-11-20 18:24:27
合計ジャッジ時間 52,186 ms
ジャッジサーバーID
（参考情報） 		judge2 / judge3
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 * 2
other TLE * 15
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 #
raw source code 

import bisect
import copy
import decimal
import fractions
import functools
import heapq
import itertools
import math
import random
import sys
from collections import Counter,deque,defaultdict
from functools import lru_cache,reduce
from heapq import heappush,heappop,heapify,heappushpop,_heappop_max,_heapify_max
def _heappush_max(heap,item):
    heap.append(item)
    heapq._siftdown_max(heap, 0, len(heap)-1)
def _heappushpop_max(heap, item):
    if heap and item < heap[0]:
        item, heap[0] = heap[0], item
        heapq._siftup_max(heap, 0)
    return item
from math import gcd as GCD
read=sys.stdin.read
readline=sys.stdin.readline
readlines=sys.stdin.readlines

def Comb(N,K,mod=0):
    if K<0 or K>N:
        return 0
    K=min(K,N-K)
    s=1
    if mod:
        for i in range(N,N-K,-1):
            s*=i
            s%=mod
        ss=1
        for i in range(1,K+1):
            ss*=i
            ss%=mod
        s*=MOD(mod).Pow(ss,-1)
        s%=mod
    else:
        for i in range(N-K+1,N+1):
            s*=i
        for i in range(1,K+1):
            s//=i
    return s

def Bernoulli_Numbers(N,mod=0):
    bernoulli_numbers=[0]*(N+1) if mod else [fractions.Fraction(0)]*(N+1)
    bernoulli_numbers[0]+=1
    if mod:
        MD=MOD(mod)
        MD.Build_Fact(N+1)
        for i in range(1,N+1):
            bernoulli_numbers[i]=-MD.Pow(i+1,-1)*sum(MD.Comb(i+1,j)*bernoulli_numbers[j] for j in range(i))%mod
    else:
        for i in range(1,N+1):
            bernoulli_numbers[i]=-sum(Comb(i+1,j)*bernoulli_numbers[j] for j in range(i))/(i+1)
    return bernoulli_numbers

class Faulhaber:
    def __init__(self,K,mod=0):
        self.K=K
        self.mod=mod
        if self.mod:
            bernoulli_numbers=Bernoulli_Numbers(self.K,self.mod)
            MD=MOD(self.mod)
            MD.Build_Fact(self.K+1)
            inve=MD.Pow(self.K+1,-1)
            self.coefficient=[bernoulli_numbers[i]*MD.Comb(self.K+1,i)*inve%mod for i in range(self.K+1)]
            for i in range(1,self.K+1,2):
                self.coefficient[i]*=-1
                self.coefficient[i]%=mod
        else:
            bernoulli_numbers=Bernoulli_Numbers(self.K)
            self.coefficient=[bernoulli_numbers[i]*Comb(self.K+1,i)/(K+1) for i in range(self.K+1)]
            for i in range(1,self.K+1,2):
                self.coefficient[i]*=-1

    def __call__(self,N):
        retu=0
        N_pow=N
        for i in range(self.K+1):
            retu+=N_pow*self.coefficient[self.K-i]
            N_pow*=N
            if self.mod:
                retu%=self.mod
                N_pow%=self.mod
        return retu

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):
        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

N,K=map(int,readline().split())
F=Faulhaber(K)
ans=F(N)
print(ans)
0