Dazzling GCD Pair NOTUNIT Solution

Dazzling GCD Pair NOTUNIT Solution

Dazzler has a task for you.

Given two positive integers A and B, find two positive integers i and j such that:

  • gcd(i,j)>1;
  • A≤i<j≤B;
  • The value (i+j) is minimum possible.

If there are multiple solutions, you may print any of them. If no such pair exists, print −1.

Input Format
First line will contain T, number of test cases. Then the test cases follow.
Each test case contains of a single line of input, two integers A and B.

Output Format
For each test case, output in a single line two space-separated integers i and j satisfying all the conditions. If no such pair exists, print −1.

Constraints
1≤T≤105
1≤A<B≤109

Sample Input 1
2
2 3
2 10

Sample Output 1
-1
2 4

Explanation

  • Test case 1: There exists no pair satisfying all the conditions.
  • Test case 2: A valid pair satisfying all the conditions is (i,j)=(2,4). The value gcd(2,4)=2>1. The value (i+j)=6.
    It can be proven that no such pair exists that satisfies all the conditions and has sum less than 6.

SOLUTION

Program: Dazzling GCD Pair NOTUNIT Solution in Python

for _ in range (int(input())):
    x,y=map(int,input().split())
    if (x%2==0):
        if(y-x>=2):
            print(x,x+2)
        else:
            print(-1)
    else:
        if(y-x >=3):
            if(x%3==0):
                print(x,x+3)
            else:
                print(x+1,x+3)
        else:
            print(-1)

Program: Dazzling GCD Pair NOTUNIT Solution in C++

#include <iostream>
using namespace std;

int main() {
	int t,a,b;
	cin>>t;
	while(t--){
	    cin>>a>>b;
	    if(a%2==0){
	        if(b>=a+2) cout<<a<<" "<<a+2;
	        else cout<<-1;
	    }
	    else{
	        if(b<a+3) cout<<-1;
	        else if(a%3==0) cout<<a<<" "<<a+3;
	        else cout<<a+1<<" "<<a+3;
	    }
	    cout<<"\n";
	}
	return 0;
}

Program: Dazzling GCD Pair NOTUNIT Solution in Java

import java.util.*;
import java.lang.*;
import java.io.*;

class Codechef
{
	public static void main (String[] args) throws java.lang.Exception
	{
		Scanner s=new Scanner(System.in);
		int n=s.nextInt();
		while(n-->0){
		    int a=s.nextInt();
		    int b=s.nextInt();
		    if(Math.abs(a-b)<2){
		        System.out.println(-1);
		    }
		    else if(a%2==0){
		        System.out.println(a+" "+(a+2));
		    }
		    else{
		        if(Math.abs(a-b)==2){
		            System.out.println(-1);
		        }
		        else if(a%3==0){
		            System.out.println(a+" "+(a+3));
		        }
		        else{
		            System.out.println((a+1)+" "+(a+3));
		        }
		    }
		}
	}
}

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