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

You are given an array x2,x3,…,xn𝑥2,𝑥3,…,𝑥𝑛. Your task is to find any array a1,…,an𝑎1,…,𝑎𝑛, where:1≤ai≤1091≤𝑎𝑖≤109 for all 1≤i≤n1≤𝑖≤𝑛.xi=aimodai−1𝑥𝑖=𝑎𝑖mod𝑎𝑖−1 for all 2≤i≤n2≤𝑖≤𝑛.Here cmodd𝑐mod𝑑 denotes the remainder of the division of the integer c𝑐 by the integer d𝑑. For example 5mod2=15mod2=1, 72mod3=072mod3=0, 143mod14=3143mod14=3.Note that if there is more than one a𝑎 which satisfies the statement, you are allowed to find any.InputThe first line contains a single integer t𝑡 (1≤t≤104)(1≤𝑡≤104) — the number of test cases.The first line of each test case contains a single integer n𝑛 (2≤n≤500)(2≤𝑛≤500) — the number of elements in a𝑎.The second line of each test case contains n−1𝑛−1 integers x2,…,xn𝑥2,…,𝑥𝑛 (1≤xi≤500)(1≤𝑥𝑖≤500) — the elements of x𝑥.It is guaranteed that the sum of values n𝑛 over all test cases does not exceed 2⋅1052⋅105.OutputFor each test case output any a1,…,an𝑎1,…,𝑎𝑛 (1≤ai≤1091≤𝑎𝑖≤109) which satisfies the statement.ExampleinputCopy542 4 131 164 2 5 1 2250031 5outputCopy3 5 4 92 5 115 14 16 5 11 24501 5002 7 5NoteIn the first test case a=[3,5,4,9]𝑎=[3,5,4,9] satisfies the conditions, because:a2moda1=5mod3=2=x2𝑎2mod𝑎1=5mod3=2=𝑥2;a3moda2=4mod5=4=x3𝑎3mod𝑎2=4mod5=4=𝑥3;a4moda3=9mod4=1=x4𝑎4mod𝑎3=9mod4=1=𝑥4;

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 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

You are given a 0-indexed integer array nums, and you are allowed to traverse between its indices. You can traverse between index i and index j, i != j, if and only if gcd(nums[i], nums[j]) > 1, where gcd is the greatest common divisor.Your task is to determine if for every pair of indices i and j in nums, where i < j, there exists a sequence of traversals that can take us from i to j.Return true if it is possible to traverse between all such pairs of indices, or false otherwise. Example 1:Input: nums = [2,3,6]Output: trueExplanation: In this example, there are 3 possible pairs of indices: (0, 1), (0, 2), and (1, 2).To go from index 0 to index 1, we can use the sequence of traversals 0 -> 2 -> 1, where we move from index 0 to index 2 because gcd(nums[0], nums[2]) = gcd(2, 6) = 2 > 1, and then move from index 2 to index 1 because gcd(nums[2], nums[1]) = gcd(6, 3) = 3 > 1.To go from index 0 to index 2, we can just go directly because gcd(nums[0], nums[2]) = gcd(2, 6) = 2 > 1. Likewise, to go from index 1 to index 2, we can just go directly because gcd(nums[1], nums[2]) = gcd(3, 6) = 3 > 1.Example 2:Input: nums = [3,9,5]Output: falseExplanation: No sequence of traversals can take us from index 0 to index 2 in this example. So, we return false.Example 3:Input: nums = [4,3,12,8]Output: trueExplanation: There are 6 possible pairs of indices to traverse between: (0, 1), (0, 2), (0, 3), (1, 2), (1, 3), and (2, 3). A valid sequence of traversals exists for each pair, so we return true.

Develop a Java program to find the GCD (Greatest Common Divisor) of two numbers.Input FormatTwo integers a and b separated by a space.ConstraintsThe absolute values of a and b will be less than or equal to 10^9. a and b are non-negative integers.Output FormatA single integer representing the GCD of a and b.Sample Input 012 18Sample Output 06Contest ends in an hourSubmissions: 0Max Score: 5Difficulty: EasyRate This Challenge: More Java 151import java.io.*;2import java.util.*;3​4public class Solution {5​6    public static void main(String[] args) {7        /* Enter your code here. Read input from STDIN. Print output to STDOUT. Your class should be named Solution. */8   }9}