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 Hadamard(polynomial,n,mod=0,inverse=False): assert mod%2 polynomial_=[x for x in polynomial]+[0]*((1<ii: continue polynomial_[i],polynomial_[ii]=polynomial_[i]+polynomial_[ii],polynomial_[i]-polynomial_[ii] if mod: polynomial_[i]%=mod polynomial_[ii]%=mod if inverse: if mod: inve_2=pow((mod+1)//2,n) for i in range(1<