You are given two distinct non-negative integers x𝑥 and y𝑦. Consider two infinite sequences a1,a2,a3,…𝑎1,𝑎2,𝑎3,… and b1,b2,b3,…𝑏1,𝑏2,𝑏3,…, wherean=n⊕x𝑎𝑛=𝑛⊕𝑥;bn=n⊕y𝑏𝑛=𝑛⊕𝑦.Here, x⊕y𝑥⊕𝑦 denotes the bitwise XOR operation of integers x𝑥 and y𝑦.For example, with x=6𝑥=6, the first 88 elements of sequence a𝑎 will look as follows: [7,4,5,2,3,0,1,14,…][7,4,5,2,3,0,1,14,…]. Note that the indices of elements start with 11.Your task is to find the length of the longest common subsegment†† of sequences a𝑎 and b𝑏. In other words, find the maximum integer m𝑚 such that ai=bj,ai+1=bj+1,…,ai+m−1=bj+m−1𝑎𝑖=𝑏𝑗,𝑎𝑖+1=𝑏𝑗+1,…,𝑎𝑖+𝑚−1=𝑏𝑗+𝑚−1 for some i,j≥1𝑖,𝑗≥1.††A subsegment of sequence p𝑝 is a sequence pl,pl+1,…,pr𝑝𝑙,𝑝𝑙+1,…,𝑝𝑟, where 1≤l≤r1≤𝑙≤𝑟.InputEach test consists of multiple test cases. The first line contains a single integer t𝑡 (1≤t≤1041≤𝑡≤104) — the number of test cases. The description of the test cases follows.The only line of each test case contains two integers x𝑥 and y𝑦 (0≤x,y≤109,x≠y0≤𝑥,𝑦≤109,𝑥≠𝑦) — the parameters of the sequences.OutputFor each test case, output a single integer — the length of the longest common subsegment.ExampleinputCopy40 112 457 37316560849 14570961outputCopy18433554432NoteIn the first test case, the first 77 elements of sequences a𝑎 and b𝑏 are as follows:a=[1,2,3,4,5,6,7,…]𝑎=[1,2,3,4,5,6,7,…]b=[0,3,2,5,4,7,6,…]𝑏=[0,3,2,5,4,7,6,…]It can be shown that there isn't a positive integer k𝑘 such that the sequence [k,k+1][𝑘,𝑘+1] occurs in b𝑏 as a subsegment. So the answer is 11.In the third test case, the first 2020 elements of sequences a𝑎 and b𝑏 are as follows:a=[56,59,58,61,60,63,62,49,48,51,50,53,52,55,54,41, 40, 43, 42,45,…]𝑎=[56,59,58,61,60,63,62,49,48,51,50,53,52,55,54,41, 40, 43, 42,45,…]b=[36,39,38,33,32,35,34,45,44,47,46,41, 40, 43, 42,53,52,55,54,49,…]𝑏=[36,39,38,33,32,35,34,45,44,47,46,41, 40, 43, 42,53,52,55,54,49,…]It can be shown that one of the longest common subsegments is the subsegment [41,40,43,42][41,40,43,42] with a length of 44.

B. XOR Sequences

You are given an array 𝐴A of size 𝑁N.You can rearrange the elements of 𝐴A as you want. After that, construct an array 𝐵B of size 𝑁N as:𝐵1=𝐴1B 1​ =A 1​ ;𝐵𝑖=𝐵𝑖−1⊕𝐴𝑖B i​ =B i−1​ ⊕A i​ for all 2≤𝑖≤𝑁2≤i≤N, where ⊕⊕ denotes the bitwise XOR operator.Find a rearrangement of 𝐴A such that 𝐵𝑖≠0B i​ =0 for all 1≤𝑖≤𝑁1≤i≤N.Input FormatThe first line of input will contain a single integer 𝑇T, denoting the number of test cases.Each test case consists of multiple lines of input.The first line of each test case contains 𝑁N, the size of the array 𝐴A.The second line of each test case contains 𝑁N space-separated integers : 𝐴1,𝐴2,…,𝐴𝑁A 1​ ,A 2​ ,…,A N​ .Output FormatFor each test case, output on a new line, 𝑁N space-separated integers denoting the rearrangement of 𝐴A satisfying the conditions.In case no such rearrangement exists, print −1−1 instead.Constraints1≤𝑇≤2⋅1041≤T≤2⋅10 4 1≤𝑁≤2⋅1051≤N≤2⋅10 5 1≤𝐴𝑖≤1091≤A i​ ≤10 9 The sum of 𝑁N over all test cases does not exceed 2⋅1052⋅10 5 .Sample 1:InputOutput431 2 351 2 3 4 531 2 211-11 2 4 3 51 2 21Explanation:Test case 11 : It can be shown that it's impossible to rearrange 𝐴A in a valid way.Test case 22 : A possible rearrangement of array 𝐴A is [1,2,4,3,5][1,2,4,3,5] and the corresponding array 𝐵B is [1,3,7,4,1][1,3,7,4,1]. Here 𝐵𝑖≠0B i​ =0 for all 1≤𝑖≤𝑁1≤i≤N.

Given N, print the XOR of all numbers between (1-N).

A certain number 1≤x≤1091≤𝑥≤109 is chosen. You are given two integers a𝑎 and b𝑏, which are the two largest divisors of the number x𝑥. At the same time, the condition 1≤a<b<x1≤𝑎<𝑏<𝑥 is satisfied.

You are given an array of integers. Find the XOR of all the pairwise sums formed by the elements of the array.Input FormatThe first line of input contains T - the number of test cases. It is followed by 2T lines, the first line contains N - the size of the array. The second line contains the elements of the array.Output FormatFor each test case, print the XOR product of all the pairwise sums of the elements from the array, separated by a newline.Constraints10 points1 <= T <= 1001 <= N <= 10000 <= A[i] <= 10540 points1 <= T <= 1001 <= N <= 1050 <= A[i] <= 105ExampleInput254 10 54 11 8615 35 25 10 15 12Output118120ExplanationTest-Case 1All the pairwise sums formed with 4 are (4 + 4), (4 + 10), (4 + 54), (4 + 11), (4 + 8) = 8, 14, 58, 15, 12All the pairwise sums formed with 10 are (10 + 4), (10 + 10), (10 + 54), (10 + 11), (10 + 8) = 14, 20, 64, 21, 18All the pairwise sums formed with 54 are (54 + 4), (54 + 10), (54 + 54), (54 + 11), (54 + 8) = 58, 64, 108, 65, 62All the pairwise sums formed with 11 are (11 + 4), (11 + 10), (11 + 54), (11 + 11), (11 + 8) = 15, 21, 65, 22, 19All the pairwise sums formed with 8 are (8 + 4), (8 + 10), (8 + 54), (8 + 11), (8 + 8) = 12, 18, 62, 19, 16XOR of all the above sums = (8 ^ 14 ^ 58 ^ 15 ^ 12) ^ (14 ^ 20 ^ 64 ^ 21 ^ 18) ^ (58 ^ 64 ^ 108 ^ 65 ^ 62) ^ (15 ^ 21 ^ 65 ^ 22 ^ 19) ^ (12 ^ 18 ^ 62 ^ 19 ^ 16) = 118