結果

問題 No.665 Bernoulli Bernoulli
ユーザー vwxyzvwxyz
提出日時 2021-08-18 05:31:57
言語 Python3
(3.12.2 + numpy 1.26.4 + scipy 1.12.0)
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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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
12,160 KB
testcase_01 AC 41 ms
12,288 KB
testcase_02 AC 79 ms
14,208 KB
testcase_03 AC 81 ms
14,464 KB
testcase_04 AC 83 ms
14,336 KB
testcase_05 AC 79 ms
14,336 KB
testcase_06 AC 79 ms
14,336 KB
testcase_07 AC 80 ms
14,208 KB
testcase_08 AC 77 ms
14,208 KB
testcase_09 AC 82 ms
14,336 KB
testcase_10 AC 79 ms
14,208 KB
testcase_11 AC 85 ms
14,464 KB
testcase_12 AC 81 ms
14,464 KB
testcase_13 AC 84 ms
14,464 KB
testcase_14 AC 84 ms
14,464 KB
testcase_15 AC 77 ms
14,208 KB
testcase_16 AC 80 ms
14,336 KB
testcase_17 AC 77 ms
14,208 KB
testcase_18 AC 80 ms
14,336 KB
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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 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