結果
問題 | No.8046 yukicoderの過去問 |
ユーザー | vwxyz |
提出日時 | 2023-04-22 06:26:15 |
言語 | PyPy3 (7.3.15) |
結果 |
TLE
|
実行時間 | - |
コード長 | 17,081 bytes |
コンパイル時間 | 353 ms |
コンパイル使用メモリ | 82,176 KB |
実行使用メモリ | 301,984 KB |
最終ジャッジ日時 | 2024-11-06 21:27:24 |
合計ジャッジ時間 | 7,040 ms |
ジャッジサーバーID (参考情報) |
judge5 / judge3 |
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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 | TLE | - |
testcase_01 | -- | - |
testcase_02 | -- | - |
testcase_03 | -- | - |
testcase_04 | -- | - |
testcase_05 | -- | - |
testcase_06 | -- | - |
testcase_07 | -- | - |
testcase_08 | -- | - |
ソースコード
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 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 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 a=digit-1 for i,x in enumerate(FFT_(polynomial01,polynomial11)): polynomial[i]-=x*a 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 for i in range(len(polynomial)): polynomial[i]%=mod return polynomial class Polynomial: def __init__(self,polynomial,max_degree=-1,eps=1e-12,mod=0): self.max_degree=max_degree if self.max_degree!=-1 and len(polynomial)>self.max_degree+1: self.polynomial=polynomial[:self.max_degree+1] else: self.polynomial=polynomial self.mod=mod self.eps=eps def __eq__(self,other): if type(other)!=Polynomial: return False if len(self.polynomial)!=len(other.polynomial): return False for i in range(len(self.polynomial)): if abs(self.polynomial[i]-other.polynomial[i])>self.eps: return False return True def __ne__(self,other): if type(other)!=Polynomial: return True if len(self.polynomial)!=len(other.polynomial): return True for i in range(len(self.polynomial)): if abs(self.polynomial[i]-other.polynomial[i])>self.eps: return True return False def __add__(self,other): assert type(other)==Polynomial summ=[0]*max(len(self.polynomial),len(other.polynomial)) for i in range(len(self.polynomial)): summ[i]+=self.polynomial[i] for i in range(len(other.polynomial)): summ[i]+=other.polynomial[i] if self.mod: for i in range(len(summ)): summ[i]%=self.mod while summ and abs(summ[-1])<self.eps: summ.pop() summ=Polynomial(summ,max_degree=self.max_degree,eps=self.eps,mod=self.mod) return summ def __sub__(self,other): assert type(other)==Polynomial diff=[0]*max(len(self.polynomial),len(other.polynomial)) for i in range(len(self.polynomial)): diff[i]+=self.polynomial[i] for i in range(len(other.polynomial)): diff[i]-=other.polynomial[i] if self.mod: for i in range(len(diff)): diff[i]%=self.mod while diff and abs(diff[-1])<self.eps: diff.pop() diff=Polynomial(diff,max_degree=self.max_degree,eps=self.eps,mod=self.mod) return diff def __mul__(self,other): if type(other)==Polynomial: if self.max_degree==-1: prod=[0]*(len(self.polynomial)+len(other.polynomial)-1) for i in range(len(self.polynomial)): for j in range(len(other.polynomial)): prod[i+j]+=self.polynomial[i]*other.polynomial[j] else: prod=[0]*min(len(self.polynomial)+len(other.polynomial)-1,self.max_degree+1) for i in range(len(self.polynomial)): for j in range(min(len(other.polynomial),self.max_degree+1-i)): prod[i+j]+=self.polynomial[i]*other.polynomial[j] if self.mod: for i in range(len(prod)): prod[i]%=self.mod while prod and abs(prod[-1])<self.eps: prod.pop() else: if self.mod: prod=[x*other%self.mod for x in self.polynomial] else: prod=[x*other for x in self.polynomial] while prod and abs(prod[-1])<self.eps: prod.pop() prod=Polynomial(prod,max_degree=self.max_degree,eps=self.eps,mod=self.mod) return prod def __matmul__(self,other): assert type(other)==Polynomial if self.mod: prod=NTT(self.polynomial,other.polynomial) else: prod=FFT(self.polynomial,other.polynomial) if self.max_degree!=-1 and len(prod)>self.max_degree+1: prod=prod[:self.max_degree+1] while prod and abs(prod[-1])<self.eps: prod.pop() prod=Polynomial(prod,max_degree=self.max_degree,eps=self.eps,mod=self.mod) return prod def __floordiv__(self,other): assert type(other)==Polynomial quot=[0]*(len(self.polynomial)-len(other.polynomial)+1) rema=[x for x in self.polynomial] if self.mod: inve=MOD(self.mod).Pow(other.polynomial[-1],-1) for i in range(len(self.polynomial)-len(other.polynomial),-1,-1): quot[i]=rema[i+len(other.polynomial)-1]*inve%self.mod for j in range(len(other.polynomial)): rema[i+j]-=quot[i]*other.polynomial[j] rema[i+j]%=self.mod else: inve=1/other.polynomial[-1] for i in range(len(self.polynomial)-len(other.polynomial),-1,-1): quot[i]=rema[i+len(other.polynomial)-1]*inve for j in range(len(other.polynomial)): rema[i+j]-=quot[i]*other.polynomial[j] quot=Polynomial(quot,max_degree=self.max_degree,eps=self.eps,mod=self.mod) return quot def __mod__(self,other): assert type(other)==Polynomial quot=[0]*(len(self.polynomial)-len(other.polynomial)+1) rema=[x for x in self.polynomial] if self.mod: inve=MOD(self.mod).Pow(other.polynomial[-1],-1) for i in range(len(self.polynomial)-len(other.polynomial),-1,-1): quot[i]=rema[i+len(other.polynomial)-1]*inve%self.mod for j in range(len(other.polynomial)): rema[i+j]-=quot[i]*other.polynomial[j] rema[i+j]%=self.mod rema.pop() else: inve=1/other.polynomial[-1] for i in range(len(self.polynomial)-len(other.polynomial),-1,-1): quot[i]=rema[i+len(other.polynomial)-1]*inve for j in range(len(other.polynomial)): rema[i+j]-=quot[i]*other.polynomial[j] rema.pop() rema=Polynomial(rema,max_degree=self.max_degree,eps=self.eps,mod=self.mod) return rema def __divmod__(self,other): assert type(other)==Polynomial quot=[0]*(len(self.polynomial)-len(other.polynomial)+1) rema=[x for x in self.polynomial] if self.mod: inve=MOD(self.mod).Pow(other.polynomial[-1],-1) for i in range(len(self.polynomial)-len(other.polynomial),-1,-1): quot[i]=rema[i+len(other.polynomial)-1]*inve%self.mod for j in range(len(other.polynomial)): rema[i+j]-=quot[i]*other.polynomial[j] rema[i+j]%=self.mod rema.pop() else: inve=1/other.polynomial[-1] for i in range(len(self.polynomial)-len(other.polynomial),-1,-1): quot[i]=rema[i+len(other.polynomial)-1]*inve for j in range(len(other.polynomial)): rema[i+j]-=quot[i]*other.polynomial[j] rema.pop() quot=Polynomial(quot,max_degree=self.max_degree,eps=self.eps,mod=self.mod) rema=Polynomial(rema,max_degree=self.max_degree,eps=self.eps,mod=self.mod) return quot,rema def __neg__(self): if self.mod: nega=Polynomial([(-x)%self.mod for x in self.polynomial],max_degree=self.max_degree,eps=self.eps,mod=self.mod) else: nega=Polynomial([-x for x in self.polynomial],max_degree=self.max_degree,eps=self.eps,mod=self.mod) return nega def __pos__(self): posi=Polynomial([x for x in self.polynomial],max_degree=self.max_degree,eps=self.eps,mod=self.mod) return posi def __bool__(self): return self.polynomial def __getitem__(self,n): if n<=len(self.polynomial)-1: return self.polynomial[n] else: return 0 def __setitem__(self,n,x): if self.mod: x%=self.mod if self.max_degree==-1 or n<=self.max_degree: if n<=len(self.polynomial)-1: self.polynomial[n]=x elif self.eps<abs(x): self.polynomial+=[0]*(n-len(self.polynomial))+[x] def __call__(self,x): retu=0 pow_x=1 for i in range(len(self.polynomial)): retu+=pow_x*self.polynomial[i] pow_x*=x if self.mod: retu%=self.mod pow_x%=self.mod return retu def __str__(self): return "["+", ".join(map(str,self.polynomial))+"]" def __truediv__(self,other): if type(other)==Polynomial: assert other.polynomial for n in range(len(other.polynomial)): if self.eps<abs(other.polynomial[n]): break assert len(self.polynomial)>n for i in range(n): assert abs(self.polynomial[i])<self.eps self_polynomial=self.polynomial[n:] other_polynomial=other.polynomial[n:] if self.mod: inve=MOD(self.mod).Pow(other_polynomial[0],-1) else: inve=1/other_polynomial[0] quot=[] for i in range(len(self_polynomial)-len(other_polynomial)+1): if self.mod: quot.append(self_polynomial[i]*inve%self.mod) else: quot.append(self_polynomial[i]*inve) for j in range(len(other_polynomial)): self_polynomial[i+j]-=other_polynomial[j]*quot[-1] if self.mod: self_polynomial[i+j]%=self.mod for i in range(max(0,len(self_polynomial)-len(other_polynomial)+1),len(self_polynomial)): if self.eps<abs(self_polynomial[i]): assert self.max_degree!=-1 self_polynomial=self_polynomial[-len(other_polynomial)+1:]+[0]*(len(other_polynomial)-1-len(self_polynomial)) while len(quot)<=self.max_degree: self_polynomial.append(0) if self.mod: quot.append(self_polynomial[0]*inve%self.mod) self_polynomial=[(self_polynomial[i]-other_polynomial[i]*quot[-1])%self.mod for i in range(1,len(self_polynomial))] else: quot.append(self_polynomial[0]*inve) self_polynomial=[(self_polynomial[i]-other_polynomial[i]*quot[-1]) for i in range(1,len(self_polynomial))] break quot=Polynomial(quot,max_degree=self.max_degree,eps=self.eps,mod=self.mod) else: assert self.eps<abs(other) if self.mod: inve=MOD(self.mod).Pow(other,-1) quot=Polynomial([x*inve%self.mod for x in self.polynomial],max_degree=self.max_degree,eps=self.eps,mod=self.mod) else: quot=Polynomial([x/other for x in self.polynomial],max_degree=self.max_degree,eps=self.eps,mod=self.mod) return quot 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)