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.*;

public class Main {
	static Scanner in;
	public static void main(String[] args) {
		in = new Scanner(System.in);

		Sieve s = new Sieve(1_000_001);
		//System.out.println(Arrays.toString(s.divisors));

		int t = in.nextInt();
		while( --t >= 0 ) {
			int n = in.nextInt();
			long k = in.nextLong();
			long m = 0;

			if( n%2 == 0 ) {
				m = n + k * 2;
			} else {
				m = n + s.divisors[n] + 2 * (k-1);
			}

			//System.out.println(s.divisors[n]);

			System.out.println(m);
		}

		in.close();
	}

	private static class Sieve {
		public int[] divisors;

		public Sieve(int n) {
			divisors = new int[n];
			sieve();
		}

		public void sieve() {
			divisors[0] = 0;
			divisors[1] = 1;

			for(int i=2; i<divisors.length; ++i) {
				while(i < divisors.length && divisors[i] != 0) ++i;
				
				for(int j=i; j<divisors.length; j+=i) {
					if( divisors[j] == 0 )
						divisors[j] = i;
				}
			}
		}

	}
}
