結果

問題 No.8046 yukicoderの過去問
コンテスト
ユーザー vwxyz
提出日時 2023-04-22 06:29:41
言語 PyPy3
(7.3.15)
結果
TLE  
実行時間 -
コード長 4,333 bytes
コンパイル時間 204 ms
コンパイル使用メモリ 81,792 KB
実行使用メモリ 308,944 KB
最終ジャッジ日時 2024-11-06 21:30:07
合計ジャッジ時間 6,671 ms
ジャッジサーバーID
（参考情報） 		judge4 / judge1
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ファイルパターン 結果
other TLE * 1 -- * 8
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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 gcd as GCD
read=sys.stdin.read
readline=sys.stdin.readline
readlines=sys.stdin.readlines

def FFT(polynomial0,polynomial1,digit=10**5):
    def DFT(polynomial,n,inverse=False):
        if inverse:
            primitive_root=[math.cos(-i*2*math.pi/(1<<n))+math.sin(-i*2*math.pi/(1<<n))*1j for i in range(1<<n)]
        else:
            primitive_root=[math.cos(i*2*math.pi/(1<<n))+math.sin(i*2*math.pi/(1<<n))*1j for i in range(1<<n)]
        if inverse:
            for bit in range(1,n+1):
                a=1<<bit-1
                for i in range(1<<n-bit):
                    for j in range(a):
                        s=i*2*a+j
                        t=s+a
                        polynomial[s],polynomial[t]=polynomial[s]+polynomial[t]*primitive_root[j<<n-bit],polynomial[s]-polynomial[t]*primitive_root[j<<n-bit]
        else:
            for bit in range(n,0,-1):
                a=1<<bit-1
                for i in range(1<<n-bit):
                    for j in range(a):
                        s=i*2*a+j
                        t=s+a
                        polynomial[s],polynomial[t]=polynomial[s]+polynomial[t],primitive_root[j<<n-bit]*(polynomial[s]-polynomial[t])

    def FFT_(polynomial0,polynomial1):
        N0=len(polynomial0)
        N1=len(polynomial1)
        N=N0+N1-1
        n=(N-1).bit_length()
        polynomial0=polynomial0+[0]*((1<<n)-N0)
        polynomial1=polynomial1+[0]*((1<<n)-N1)
        DFT(polynomial0,n)
        DFT(polynomial1,n)
        fft=[x*y for x,y in zip(polynomial0,polynomial1)]
        DFT(fft,n,inverse=True)
        fft=[round((fft[i]/(1<<n)).real) for i in range(N)]
        return fft

    N0=len(polynomial0)
    N1=len(polynomial1)
    N=N0+N1-1
    polynomial00,polynomial01=[None]*N0,[None]*N0
    polynomial10,polynomial11=[None]*N1,[None]*N1
    for i in range(N0):
        polynomial00[i],polynomial01[i]=divmod(polynomial0[i],digit)
    for i in range(N1):
        polynomial10[i],polynomial11[i]=divmod(polynomial1[i],digit)
    polynomial=[0]*(N)
    a=digit**2-digit
    for i,x in enumerate(FFT_(polynomial00,polynomial10)):
        polynomial[i]+=x*a%mod
    a=digit-1
    for i,x in enumerate(FFT_(polynomial01,polynomial11)):
        polynomial[i]-=x*a%mod
    for i,x in enumerate(FFT_([x1+x2 for x1,x2 in zip(polynomial00,polynomial01)],[x1+x2 for x1,x2 in zip(polynomial10,polynomial11)])):
        polynomial[i]+=x*digit%mod
        polynomial[i]%=mod
    return polynomial

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)):
                    x=poly_nume[i]*poly_deno[j]
                    if mod:
                        x%=mod
                    conv[i+j]+=x
            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]

N=int(readline())
K=int(readline())
mod=10**9+7
nume=[1]
deno=[0]*(10**5+1)
deno[0]=1
for x in map(int,readline().split()):
    deno[x]=mod-1
ans=Bostan_Mori(nume,deno,N,mod=10**9+7,fft=True)
print(ans)
0