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.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.lang.reflect.Array;
import java.util.*;

public class Main {

    public static void main(String[] args) throws IOException {
        int test = GetInput.getInt();
        while(test-->0){
            long []ins = GetInput.getLongArrayInput();
            long n = ins[0]; long k = ins[1];

            while(k>0){
                if (n%2==0){
                    n = n + k*2;
                    k = 0;
                }
                else {
                    for (int i = 3; i <= n; i+=2 ){
                        if (n%i == 0){
                            n = n + i;
                            k--;
                            break;
                        }
                    }
                }
            }

            System.out.println(n);
        }

    }
}


class GetInput {
    static BufferedReader bufferedReader = new BufferedReader(new InputStreamReader(System.in));

    static char[] getCharArray() {
        char[] charArray;
        try {
            StringBuilder string = getInputString();
            charArray = new char[string.length()];
            for (int i = 0; i < string.length(); i++) {
                charArray[i] = string.charAt(i);
            }
            return charArray;
        } catch (Exception e) {
            e.printStackTrace();
        }
        charArray = new char[0];
        return charArray;
    }

    static int[] getArrayInt() {
        String[] string;
        int[] array;
        try {
            string = bufferedReader.readLine().split("\\s+");
            array = new int[string.length];
            for (int i = 0; i < string.length; i++) {
                array[i] = Integer.parseInt(string[i]);
            }
            return array;
        } catch (IOException e) {
            e.printStackTrace();
        }

        int[] arra = new int[2];
        return arra;
    }

    static int getInt() {
        try {
            String string = bufferedReader.readLine();
            return Integer.parseInt(string);
        } catch (IOException e) {
            e.printStackTrace();
        }

        return 0;
    }

    static StringBuilder getInputString() {
        try {
            StringBuilder string = new StringBuilder();
            string.append(bufferedReader.readLine());
            return string;
        } catch (IOException e) {
            e.printStackTrace();
        }
        return new StringBuilder();
    }

    static long getLongInput() {
        try {
            String string = bufferedReader.readLine();
            return Long.parseLong(string);
        } catch (IOException e) {
            e.printStackTrace();
        }

        return 0;
    }

    static long[] getLongArrayInput() {
        String[] string;
        long[] array;
        try {
            string = bufferedReader.readLine().split("\\s+");
            array = new long[string.length];
            for (int i = 0; i < string.length; i++) {
                array[i] = Long.parseLong(string[i]);
            }
            return array;
        } catch (IOException e) {
            e.printStackTrace();
        }

        long[] arra = new long[2];
        return arra;
    }
}
