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.lang.*;
import java.util.*;
import java.io.*;
public class Main {
	static int a[]=new int[1000001];
    public static void prime(long n)
    {
    	a[2]=1;
    	for(long i=3;i<=n;i+=2)
    	{
    		a[(int)i]=1;
    	}
    	for(long i=3;i<=n;i+=2)
    	{
    		if(a[(int)i]==1)
    		{
    			for(long j=i*i;j<=n;j+=i)
    			{
    				a[(int)j]=0;
    			}
    		}
    	}
    }
    public static void main(String args[]) throws Exception{
        BufferedReader b=new BufferedReader(new InputStreamReader(System.in));
        int t=Integer.parseInt(b.readLine());
        prime(1000000);
        while(t!=0)
        {
            String []v=b.readLine().split(" ");
            long n=Long.parseLong(v[0]);
            long k=Long.parseLong(v[1]);
            long x=n,p=2;
            while(k!=0)
            {
                if(a[(int)n]!=0)
                {
                	n=n*2;
                	k--;
                	n=n+2*k;
                	k=0;
                }
                else if(n%2==0)
                {
                	n=n+2*k;
                	k=0;
                }
                else
                {
                	for(int i=3;i<=n;i+=2)
                    {
                        if(n%i==0)
                        {
                            n=n+i;
                            k--;
                            break;
                        }
                    }
                    n=n+2*k;
                    k=0;
                }
            }
            System.out.println(n);
            t--;
        }
    }
}