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.*;
import java.io.*;
public class Main {
    static class Scan {
        private byte[] buf=new byte[1024];
        private int index;
        private InputStream in;
        private int total;
        public Scan()
        {
            in=System.in;
        }
        public int scan()throws IOException
        {
            if(total<0)
            throw new InputMismatchException();
            if(index>=total)
            {
                index=0;
                total=in.read(buf);
                if(total<=0)
                return -1;
            }
            return buf[index++];
        }
        public int scanInt()throws IOException
        {
            int integer=0;
            int n=scan();
            while(isWhiteSpace(n))
            n=scan();
            int neg=1;
            if(n=='-')
            {
                neg=-1;
                n=scan();
            }
            while(!isWhiteSpace(n))
            {
                if(n>='0'&&n<='9')
                {
                    integer*=10;
                    integer+=n-'0';
                    n=scan();
                }
                else throw new InputMismatchException();
            }
            return neg*integer;
        }
        public double scanDouble()throws IOException
        {
            double doub=0;
            int n=scan();
            while(isWhiteSpace(n))
            n=scan();
            int neg=1;
            if(n=='-')
            {
                neg=-1;
                n=scan();
            }
            while(!isWhiteSpace(n)&&n!='.')
            {
                if(n>='0'&&n<='9')
                {
                    doub*=10;
                    doub+=n-'0';
                    n=scan();
                }
                else throw new InputMismatchException();
            }
            if(n=='.')
            {
                n=scan();
                double temp=1;
                while(!isWhiteSpace(n))
                {
                    if(n>='0'&&n<='9')
                    {
                        temp/=10;
                        doub+=(n-'0')*temp;
                        n=scan();
                    }
                    else throw new InputMismatchException();
                }
            }
            return doub*neg;
        }
        public String scanString()throws IOException
        {
            StringBuilder sb=new StringBuilder();
            int n=scan();
            while(isWhiteSpace(n))
            n=scan();
            while(!isWhiteSpace(n))
            {
                sb.append((char)n);
                n=scan();
            }
            return sb.toString();
        }
        private boolean isWhiteSpace(int n)
        {
            if(n==' '||n=='\n'||n=='\r'||n=='\t'||n==-1)
            return true;
            return false;
        }
    }
    public static void main(String args[]) throws IOException {
        Scan input=new Scan();
        int test=input.scanInt();
        for(int t=1;t<=test;t++) {
            long n=input.scanInt();
            long k=input.scanInt();
            long ans=n;
            while(k!=0) {
                if(ans%2==0) {
                    ans+=2*k;
                    break;
                }
                ans+=get_min(ans);
                k--;
            }
            System.out.println(ans);
        }
    }
    public static long get_min(long n) {
        long lim=(long)Math.sqrt(n);
        for(int i=3;i<=lim;i+=2) {
            if(n%i==0) {
                return i;
            }
        }
        return n;
    }
}
