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 #import pypyjit #pypyjit.set_param('max_unroll_recursion=-1') #sys.set_int_max_str_digits(10**9) def Factorize(N): assert N>=1 factors=defaultdict(int) for p in range(2,N): if p**2>N: break while N%p==0: factors[p]+=1 N//=p if N!=1: factors[N]+=1 return factors class Cumsum: def __init__(self,lst,mod=0): self.N=len(lst) self.mod=mod self.cumsum=[0]*(self.N+1) self.cumsum[0]=0 for i in range(1,self.N+1): self.cumsum[i]=self.cumsum[i-1]+lst[i-1] if self.mod: self.cumsum[i]%=self.mod def __getitem__(self,i): if type(i)==int: if 0<=i