結果

問題 No.665 Bernoulli Bernoulli
ユーザー vwxyzvwxyz
提出日時 2021-08-27 17:11:35
言語 Python3
(3.12.2 + numpy 1.26.4 + scipy 1.12.0)
結果
TLE  
実行時間 -
コード長 4,535 bytes
コンパイル時間 89 ms
コンパイル使用メモリ 13,440 KB
実行使用メモリ 19,360 KB
最終ジャッジ日時 2024-04-30 20:35:11
合計ジャッジ時間 3,767 ms
ジャッジサーバーID
（参考情報） 		judge5 / judge1
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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 38 ms
19,232 KB
testcase_01 AC 35 ms
12,288 KB
testcase_02 TLE -
testcase_03 -- -
testcase_04 -- -
testcase_05 -- -
testcase_06 -- -
testcase_07 -- -
testcase_08 -- -
testcase_09 -- -
testcase_10 -- -
testcase_11 -- -
testcase_12 -- -
testcase_13 -- -
testcase_14 -- -
testcase_15 -- -
testcase_16 -- -
testcase_17 -- -
testcase_18 -- -
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 # 

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