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.max_degree+1: prod=prod[:self.max_degree+1] while prod and abs(prod[-1])n for i in range(n): assert abs(self.polynomial[i])