結果

問題 No.665 Bernoulli Bernoulli
コンテスト
ユーザー vwxyz
提出日時 2021-08-18 05:31:57
言語 Python3
(3.13.1 + numpy 2.2.1 + scipy 1.14.1)
結果
AC  
実行時間 85 ms / 2,000 ms
コード長 4,499 bytes
コンパイル時間 135 ms
コンパイル使用メモリ 13,056 KB
実行使用メモリ 14,464 KB
最終ジャッジ日時 2024-10-11 12:44:53
合計ジャッジ時間 2,826 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 * 4
other AC * 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 degrees, gcd as GCD
read=sys.stdin.read
readline=sys.stdin.readline
readlines=sys.stdin.readlines

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

class Lagrange_Interpolation:
    def __init__(self,X=False,Y=False,x0=None,xd=None,mod=0):
        self.degree=len(Y)-1
        self.mod=mod
        assert self.degree<self.mod
        if x0!=None and xd!=None:
            assert xd>0
            self.X=[(x0+i*xd)%self.mod for i in range(self.degree+1)]
            fact_inve=1
            for i in range(1,self.degree+1):
                fact_inve*=i*xd
                fact_inve%=self.mod
            fact_inve=MOD(self.mod).Pow(fact_inve,-1)
            self.coefficient=[y for y in Y]
            for i in range(self.degree-1,-1,-2):
                self.coefficient[i]*=-1
            for i in range(self.degree,-1,-1):
                self.coefficient[i]*=fact_inve
                self.coefficient[i]%=self.mod
                self.coefficient[self.degree-i]*=fact_inve
                self.coefficient[self.degree-i]%=self.mod
                fact_inve*=i*xd
                fact_inve%=self.mod        
        else:
            self.X=X
            assert len(self.X)==self.degree+1
            self.coefficient=[y for y in Y]
            for i in range(self.degree+1):
                for j in range(self.degree+1):
                    if i==j:
                        continue
                    self.coefficient[i]*=X[i]-X[j]
                    self.coefficient%=self.mod

    def __getitem__(self,N):
        N%=self.mod
        XX=[N-x for x in self.X]
        XX_left=[1]*(self.degree+2)
        for i in range(1,self.degree+2):
            XX_left[i]=XX_left[i-1]*XX[i-1]%self.mod
        XX_right=[1]*(self.degree+2)
        for i in range(self.degree,-1,-1):
            XX_right[i]=XX_right[i+1]*XX[i]%self.mod
        return sum(XX_left[i]*XX_right[i+1]*self.coefficient[i] for i in range(self.degree+1))%self.mod

N,K=map(int,readline().split())
mod=10**9+7
Y=[0]
for i in range(1,K+2):
    Y.append((Y[-1]+pow(i,K,mod))%mod)
LI=Lagrange_Interpolation(Y=Y,x0=0,xd=1,mod=mod)
ans=LI[N]
print(ans)
0