結果
問題 | No.980 Fibonacci Convolution Hard |
ユーザー | vwxyz |
提出日時 | 2023-04-06 07:50:01 |
言語 | PyPy3 (7.3.15) |
結果 |
AC
|
実行時間 | 755 ms / 2,000 ms |
コード長 | 19,346 bytes |
コンパイル時間 | 244 ms |
コンパイル使用メモリ | 82,560 KB |
実行使用メモリ | 237,768 KB |
最終ジャッジ日時 | 2024-10-02 08:46:26 |
合計ジャッジ時間 | 16,237 ms |
ジャッジサーバーID (参考情報) |
judge1 / judge5 |
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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 | 738 ms
237,092 KB |
testcase_01 | AC | 750 ms
236,728 KB |
testcase_02 | AC | 742 ms
237,032 KB |
testcase_03 | AC | 737 ms
237,740 KB |
testcase_04 | AC | 744 ms
237,372 KB |
testcase_05 | AC | 740 ms
237,712 KB |
testcase_06 | AC | 755 ms
236,760 KB |
testcase_07 | AC | 750 ms
236,904 KB |
testcase_08 | AC | 741 ms
236,872 KB |
testcase_09 | AC | 751 ms
237,148 KB |
testcase_10 | AC | 744 ms
236,632 KB |
testcase_11 | AC | 743 ms
237,404 KB |
testcase_12 | AC | 732 ms
236,692 KB |
testcase_13 | AC | 745 ms
237,768 KB |
testcase_14 | AC | 736 ms
237,740 KB |
testcase_15 | AC | 735 ms
237,356 KB |
testcase_16 | AC | 706 ms
237,452 KB |
ソースコード
import bisect import copy import decimal import fractions import heapq import itertools import math import random import sys import time 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 write=sys.stdout.write class Polynomial: def __init__(self,polynomial,max_degree=-1,eps=0,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 self.eps<abs(self.polynomial[i]-other.polynomial[i]): 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 self.eps<abs(self.polynomial[i]-other.polynomial[i]): return True return False def __add__(self,other): if 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 else: summ=[x for x in self.polynomial] if self.polynomial else [0] summ[0]+=other if self.mod: summ[0]%=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): if 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 else: diff=[x for x in self.polynomial] if self.polynomial else [0] diff[0]-=other if self.mod: diff[0]%=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 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 __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 __rtruediv__(self,other): assert self.polynomial and self.eps<self.polynomial[0] assert self.max_degree!=-1 if self.mod: quot=[MOD(self.mod).Pow(self.polynomial[0],-1)] if self.mod==998244353: prim_root=3 prim_root_inve=332748118 else: prim_root=Primitive_Root(self.mod) prim_root_inve=MOD(self.mod).Pow(prim_root,-1) def DFT(polynomial,n,inverse=False): polynomial=polynomial+[0]*((1<<n)-len(polynomial)) if inverse: for bit in range(1,n+1): a=1<<bit-1 x=pow(prim_root,mod-1>>bit,mod) U=[1] for _ in range(a): U.append(U[-1]*x%mod) 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]*U[j])%mod,(polynomial[s]-polynomial[t]*U[j])%mod x=pow((mod+1)//2,n,mod) for i in range(1<<n): polynomial[i]*=x polynomial[i]%=mod else: for bit in range(n,0,-1): a=1<<bit-1 x=pow(prim_root_inve,mod-1>>bit,mod) U=[1] for _ in range(a): U.append(U[-1]*x%mod) 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])%mod,U[j]*(polynomial[s]-polynomial[t])%mod return polynomial else: quot=[1/self.polynomial[0]] def DFT(polynomial,n,inverse=False): N=len(polynomial) 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)] polynomial=polynomial+[0]*((1<<n)-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] for i in range(1<<n): polynomial[i]=round((polynomial[i]/(1<<n)).real) 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]) return polynomial for n in range(self.max_degree.bit_length()): prev=quot if self.mod: polynomial=[x*y*y%self.mod for x,y in zip(DFT(self.polynomial[:1<<n+1],n+2),DFT(prev,n+2))] quot=DFT(polynomial,n+2,inverse=True)[:1<<n+1] else: polynomial=[x*y*y for x,y in zip(DFT(self.polynomial[:1<<n+1],n+2),DFT(prev,n+2))] quot=DFT(polynomial,n+2,inverse=True)[:1<<n+1] for i in range(1<<n): quot[i]=2*prev[i]-quot[i] if self.mod: quot[i]%=self.mod for i in range(1<<n,1<<n+1): quot[i]=-quot[i] if self.mod: quot[i]%=self.mod quot=quot[:self.max_degree+1] for i in range(len(quot)): quot[i]*=other if self.mod: quot[i]%=self.mod return quot 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 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] while rema and abs(rema[-1])<=self.eps: 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 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] while rema and abs(rema[-1])<=self.eps: 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 type(n)==int: if n<=len(self.polynomial)-1: return self.polynomial[n] else: return 0 else: return Polynomial(polynomial=self.polynomial[n],max_degree=self.max_degree,eps=self.eps,mod=self.mod) def __setitem__(self,n,a): if self.mod: a%=self.mod if self.max_degree==-1 or n<=self.max_degree: if n<=len(self.polynomial)-1: self.polynomial[n]=a elif self.eps<abs(a): self.polynomial+=[0]*(n-len(self.polynomial))+[a] def __iter__(self): for x in self.polynomial: yield 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 Degree(self): return len(self.polynomial)-1 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=None): self.p=p self.e=e if self.e==None: self.mod=self.p else: 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] if self.e==None: for i in range(1,N+1): self.factorial.append(self.factorial[-1]*i%self.mod) else: self.cnt=[0]*(N+1) for i in range(1,N+1): self.cnt[i]=self.cnt[i-1] ii=i 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 retu=self.factorial[N] if self.e!=None and self.cnt[N]: retu*=pow(self.p,self.cnt[N],self.mod)%self.mod retu%=self.mod return retu def Fact_Inve(self,N): if self.e!=None and 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.mod*self.factorial_inve[N-K]%self.mod if self.e!=None: 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 P=int(readline()) mod=10**9+7 A=[0,1,P,(P*2+1)%mod] A=[sum(A[j]*A[i-j]%mod for j in range(i+1))%mod for i in range(4)] deno=Polynomial([1,(-2*P)%mod,(P**2-2)%mod,2*P%mod,1],mod=mod,max_degree=2*10**6) nume=Polynomial([sum(A[j]*deno[(i-j)] for j in range(i+1))%mod for i in range(4)],mod=mod,max_degree=2*10**6) poly=nume/deno Q=int(readline()) for q in range(Q): k=int(readline())-2 ans=poly[k] print(ans)