Orac is studying number theory, and he is interested in the properties of divisors.

For two positive integers a and b, a is a divisor of b if and only if there exists an integer c, such that a⋅ c=b.

For n ≥ 2, we will denote as f(n) the smallest positive divisor of n, except 1.

For example, f(7)=7,f(10)=2,f(35)=5.

For the fixed integer n, Orac decided to add f(n) to n. 

For example, if he had an integer n=5, the new value of n will be equal to 10. And if he had an integer n=6, n will be changed to 8.

Orac loved it so much, so he decided to repeat this operation several times.

Now, for two positive integers n and k, Orac asked you to add f(n) to n exactly k times (note that n will change after each operation, so f(n) may change too) and tell him the final value of n.

For example, if Orac gives you n=5 and k=2, at first you should add f(5)=5 to n=5, so your new value of n will be equal to n=10, after that, you should add f(10)=2 to 10, so your new (and the final!) value of n will be equal to 12.

Orac may ask you these queries many times.

Input

The first line of the input is a single integer t\ (1≤ t≤ 100): the number of times that Orac will ask you.

Each of the next t lines contains two positive integers n,k\ (2≤ n≤ 10^6, 1≤ k≤ 10^9), corresponding to a query by Orac.

It is guaranteed that the total sum of n is at most 10^6. 

Output

Print t lines, the i-th of them should contain the final value of n in the i-th query by Orac.

Example

Input


3
5 1
8 2
3 4


Output


10
12
12

Note

In the first query, n=5 and k=1. The divisors of 5 are 1 and 5, the smallest one except 1 is 5. Therefore, the only operation adds f(5)=5 to 5, and the result is 10.

In the second query, n=8 and k=2. The divisors of 8 are 1,2,4,8, where the smallest one except 1 is 2, then after one operation 8 turns into 8+(f(8)=2)=10. The divisors of 10 are 1,2,5,10, where the smallest one except 1 is 2, therefore the answer is 10+(f(10)=2)=12.

In the third query, n is changed as follows: 3 → 6 → 8 → 10 → 12.
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.HashMap;
import java.util.HashSet;
import java.util.List;
import java.util.Map;
import java.util.Objects;
import java.util.Scanner;
import java.util.Set;


public class Main {


    static void solve() {
        Scanner scan = new Scanner(System.in);
        int t = scan.nextInt();
        for(int i=0;i<t;i++) {
            int n = scan.nextInt();
            int k = scan.nextInt();

            scase(n,k);
        }


//        for (int i = 0; i < t; i++) {
//            int n = scan.nextInt();
//            int k = scan.nextInt();
//            scase(n,k);
////            System.out.println(res);
////            solveCase(i, x,y,s);
//        }
    }


//    static void solveCase(int t, int x, String s) {
//
//    }


    static int getDiv(int n) {
        if(n%2 == 0) {
            return 2;
        } else{
            for(int i=3;i*i<=n;i++) {
                if(n%i == 0) {
                    return i;
                }
            }
        }
        return n;
    }


    static void scase(int n, int k) {
        if(n%2 == 0) {
            System.out.println(n+2*k);
        }else{
            int div = getDiv(n);
            n = n+div;
            if(k==1) {
                System.out.println(n);
            }else{
                int val = n + (k-1)*2;
                System.out.println(val);
            }
        }
    }





    public static void main(String[] args) {



        solve();

        //        Main m = new Main();
        //        Scanner scan = new Scanner(System.in);

        //        long n = scan.nextLong();
        //        long r = scan.nextLong();
        //        List<Long> list = new ArrayList<>();
        ////        int[] arr = new int[n];
        //        for (long i=0;i<n;i++){
        //            list.add(scan.nextLong());
        //        }
//            System.out.println(ch);
        //        solve(n, arr);
        //        scan.close();
    }


//
//    class Counter extends HashMap<Integer, Integer> {
//        public int get(int k) {
//            return containsKey(k) ? super.get(k) : 0;
//        }
//
//        public void add(int k, int v) {
//            put(k, get(k) + v);
//        }
//    }


//    static class Node {
//        int val;
//        Node next;
//        Node random;
//
//        public Node(int val) {
//            this.val = val;
//            this.next = null;
//            this.random = null;
//        }
//    }

//    static class Node {
//        int key;
//        int data;
//        Node next;
//        Node prev;
//
//        Node(int key, int data) {
//            this.key = key;
//            this.data = data;
//        }
//    }

    static class TreeNode {
        int val;
        TreeNode left;
        TreeNode right;

        TreeNode(int x) {
            val = x;
        }
    }
}
