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 | 2021-08-30 21:13:48 |
| 言語 | PyPy3 (7.3.15) |
| 結果 |
TLE
|
| 実行時間 | - |
| コード長 | 13,611 bytes |
| コンパイル時間 | 144 ms |
| コンパイル使用メモリ | 81,828 KB |
| 実行使用メモリ | 276,536 KB |
| 最終ジャッジ日時 | 2024-11-24 04:51:15 |
| 合計ジャッジ時間 | 31,022 ms |
|
ジャッジサーバーID （参考情報） |
judge3 / judge4 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| other | TLE * 9 |
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
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
N=int(readline())
K=int(readline())
mod=10**9+7
P=Polynomial([0]*(10**5+1),mod=10**9+7)
P[0]=1
for x in map(int,readline().split()):
P[x]=mod-1
P=Polynomial([1],max_degree=10**5,mod=10**9+7)/P
ans=P[N]
print(ans)