結果

問題 No.1559 Next Rational
ユーザー vwxyz
提出日時 2021-10-22 02:03:42
言語 Python3
(3.13.1 + numpy 2.2.1 + scipy 1.14.1)
結果
AC  
実行時間 43 ms / 2,000 ms
コード長 3,736 bytes
コンパイル時間 162 ms
コンパイル使用メモリ 12,928 KB
実行使用メモリ 12,160 KB
最終ジャッジ日時 2024-09-22 01:21:19
合計ジャッジ時間 1,908 ms
ジャッジサーバーID
（参考情報） 		judge3 / 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 * 3
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 #
プレゼンテーションモードにする

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 Bostan_Mori(poly_nume,poly_deno,N,mod=0,fft=False,ntt=False):
    if ntt:
        convolve=NTT
    elif fft:
        convolve=FFT
    else:
        def convolve(poly_nume,poly_deno):
            conv=[0]*(len(poly_nume)+len(poly_deno)-1)
            for i in range(len(poly_nume)):
                for j in range(len(poly_deno)):
                    conv[i+j]+=poly_nume[i]*poly_deno[j]
            if mod:
                for i in range(len(conv)):
                    conv[i]%=mod
            return conv
    while N:
        poly_deno_=[-x if i%2 else x for i,x in enumerate(poly_deno)]
        if N%2:
            poly_nume=convolve(poly_nume,poly_deno_)[1::2]
        else:
            poly_nume=convolve(poly_nume,poly_deno_)[::2]
        poly_deno=convolve(poly_deno,poly_deno_)[::2]
        if fft and mod:
            for i in range(len(poly_nume)):
                poly_nume[i]%=mod
            for i in range(len(poly_deno)):
                poly_deno[i]%=mod
        N//=2
    return poly_nume[0]
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):
        if N<0:
            return 0
        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,A,B,K=map(int,readline().split())
mod=10**9+7
MD=MOD(mod)
x=(A**2+B**2+K)*MD.Pow(A*B,-1)%mod
ans=Bostan_Mori([A,(B-A*x)%mod],[1,(-x)%mod,1],N-1,mod=mod)
print(ans)
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