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.

We say that an integer 𝐷D is a divisor of another integer 𝐴A if the fraction 𝐴/𝐷A/D is also an integer. Given two positive integers 𝐴A and 𝐵B, compute the largest number which is a divisor of both 𝐴A and 𝐵B.

You are given an integer x𝑥. Your task is to find any integer y𝑦 (1≤y<x)(1≤𝑦<𝑥) such that gcd(x,y)+ygcd(𝑥,𝑦)+𝑦 is maximum possible.Note that if there is more than one y𝑦 which satisfies the statement, you are allowed to find any.gcd(a,b)gcd(𝑎,𝑏) is the Greatest Common Divisor of a𝑎 and b𝑏. For example, gcd(6,4)=2gcd(6,4)=2.InputThe first line contains a single integer t𝑡 (1≤t≤10001≤𝑡≤1000) — the number of test cases.Each of the following t𝑡 lines contains a single integer x𝑥 (2≤x≤10002≤𝑥≤1000).OutputFor each test case, output any y𝑦 (1≤y<x1≤𝑦<𝑥), which satisfies the statement.ExampleinputCopy710721100210006outputCopy56189817503

Let's consider all integers in the range from 11 to n𝑛 (inclusive).Among all pairs of distinct integers in this range, find the maximum possible greatest common divisor of integers in pair. Formally, find the maximum value of gcd(a,b)gcd(𝑎,𝑏), where 1≤a<b≤n1≤𝑎<𝑏≤𝑛.The greatest common divisor, gcd(a,b)gcd(𝑎,𝑏), of two positive integers a𝑎 and b𝑏 is the biggest integer that is a divisor of both a𝑎 and b𝑏.InputThe first line contains a single integer t𝑡 (1≤t≤1001≤𝑡≤100)  — the number of test cases. The description of the test cases follows.The only line of each test case contains a single integer n𝑛 (2≤n≤1062≤𝑛≤106).OutputFor each test case, output the maximum value of gcd(a,b)gcd(𝑎,𝑏) among all 1≤a<b≤n1≤𝑎<𝑏≤𝑛.

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.

For k𝑘 positive integers x1,x2,…,xk𝑥1,𝑥2,…,𝑥𝑘, the value gcd(x1,x2,…,xk)gcd(𝑥1,𝑥2,…,𝑥𝑘) is the greatest common divisor of the integers x1,x2,…,xk𝑥1,𝑥2,…,𝑥𝑘 — the largest integer z𝑧 such that all the integers x1,x2,…,xk𝑥1,𝑥2,…,𝑥𝑘 are divisible by z𝑧.You are given three arrays a1,a2,…,an𝑎1,𝑎2,…,𝑎𝑛, b1,b2,…,bn𝑏1,𝑏2,…,𝑏𝑛 and c1,c2,…,cn𝑐1,𝑐2,…,𝑐𝑛 of length n𝑛, containing positive integers.You also have a machine that allows you to swap ai𝑎𝑖 and bi𝑏𝑖 for any i𝑖 (1≤i≤n1≤𝑖≤𝑛). Each swap costs you ci𝑐𝑖 coins.Find the maximum possible value ofgcd(a1,a2,…,an)+gcd(b1,b2,…,bn)gcd(𝑎1,𝑎2,…,𝑎𝑛)+gcd(𝑏1,𝑏2,…,𝑏𝑛)that you can get by paying in total at most d𝑑 coins for swapping some elements. The amount of coins you have changes a lot, so find the answer to this question for each of the q𝑞 possible values d1,d2,…,dq𝑑1,𝑑2,…,𝑑𝑞.InputThere are two integers on the first line — the numbers n𝑛 and q𝑞 (1≤n≤5⋅1051≤𝑛≤5⋅105, 1≤q≤5⋅1051≤𝑞≤5⋅105).On the second line, there are n𝑛 integers — the numbers a1,a2,…,an𝑎1,𝑎2,…,𝑎𝑛 (1≤ai≤1081≤𝑎𝑖≤108).On the third line, there are n𝑛 integers — the numbers b1,b2,…,bn𝑏1,𝑏2,…,𝑏𝑛 (1≤bi≤1081≤𝑏𝑖≤108).On the fourth line, there are n𝑛 integers — the numbers c1,c2,…,cn𝑐1,𝑐2,…,𝑐𝑛 (1≤ci≤1091≤𝑐𝑖≤109).On the fifth line, there are q𝑞 integers — the numbers d1,d2,…,dq𝑑1,𝑑2,…,𝑑𝑞 (0≤di≤10150≤𝑑𝑖≤1015).OutputPrint q𝑞 integers — the maximum value you can get for each of the q𝑞 possible values d𝑑.ExamplesinputCopy3 41 2 34 5 61 1 10 1 2 3outputCopy2 3 3 3 inputCopy5 53 4 6 8 48 3 4 9 310 20 30 40 505 55 13 1000 113outputCopy2 7 3 7 7 inputCopy1 13450outputCopy7