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.

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.

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}

The extended Euclid’s algorithm determines not only the greatest commondivisor d of two positive integers m and n but also integers (not necessarilypositive) x and y, such that mx + ny = d.a. Look up a description of the extended Euclid’s algorithm (see, e.g., [KnuI,p. 13]) and implement it in the language of your choice.b. Modify your program to find integer solutions to the Diophantine equationax + by = c with any set of integer coefficients a, b, and c

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.