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.File;
import java.io.FileInputStream;
import java.io.FileNotFoundException;
import java.io.IOException;
import java.io.PrintWriter;
import java.security.AccessControlException;
import java.util.Arrays;
import java.util.Collection;
import java.util.List;
import java.util.Scanner;
import java.util.function.Function;
import java.util.stream.Collectors;
public class _p001350A {
    static public void main(final String[] args) throws IOException {
        p001350A._main(args);
    }
//begin p001350A.java
static private class p001350A extends Solver{public p001350A(){nameIn="in/900/p001350A.in"
;}int n;int k;@Override protected void solve(){long res=n;l:for(int j=0;j<k;j++)
{for(int i=2;i<=res;i++){if(res % i==0){if(i==2){res+=1l*i*(k-j);break l;}res+=1l
*i;break;}}}pw.println(res);}@Override public void readInput()throws IOException
{n=sc.nextInt();k=sc.nextInt();if(sc.hasNextLine()){sc.nextLine();}}static public
void _main(String[]args)throws IOException{new p001350A().run();}}
//end p001350A.java
//begin net/leksi/contest/Solver.java
static private abstract class Solver{protected String nameIn=null;protected String
nameOut=null;protected boolean singleTest=false;protected boolean preprocessDebug
=false;protected boolean doNotPreprocess=false;protected Scanner sc=null;protected
PrintWriter pw=null;private void process()throws IOException{if(!singleTest){int
t=lineToIntArray()[0];while(t-->0){readInput();solve();}}else{readInput();solve(
);}}abstract protected void readInput()throws IOException;abstract protected void
solve()throws IOException;protected int[]lineToIntArray()throws IOException{return
Arrays.stream(sc.nextLine().trim().split("\\s+")).mapToInt(Integer::valueOf).toArray
();}protected long[]lineToLongArray()throws IOException{return Arrays.stream(sc.nextLine
().trim().split("\\s+")).mapToLong(Long::valueOf).toArray();}protected String joinToString
(final int[]a){return Arrays.stream(a).mapToObj(Integer::toString).collect(Collectors
.joining(" "));}protected String joinToString(final long[]a){return Arrays.stream
(a).mapToObj(Long::toString).collect(Collectors.joining(" "));}protected<T>String
joinToString(final T[]a){return Arrays.stream(a).map(v->v.toString()).collect(Collectors
.joining(" "));}protected<T>String joinToString(final T[]a,final Function<T,String>
toString){return Arrays.stream(a).map(v->v.toString()).collect(Collectors.joining
(" "));}protected<T>String joinToString(final Collection<T>a){return a.stream().map
(v->v.toString()).collect(Collectors.joining(" "));}protected<T>String joinToString
(final Collection<T>a,final Function<T,String>toString){return a.stream().map(v->
toString.apply(v)).collect(Collectors.joining(" "));}protected List<Long>intArrayToLongList
(final int[]a){return Arrays.stream(a).mapToObj(Long::valueOf).collect(Collectors
.toList());}protected List<Integer>toList(final int[]a){return Arrays.stream(a).mapToObj
(Integer::valueOf).collect(Collectors.toList());}protected List<Long>toList(final
long[]a){return Arrays.stream(a).mapToObj(Long::valueOf).collect(Collectors.toList
());}protected void run()throws IOException{boolean done=false;try{if(nameIn !=null
&&new File(nameIn).exists()){try(FileInputStream fis=new FileInputStream(nameIn)
;PrintWriter pw0=select_output();){done=true;sc=new Scanner(fis);pw=pw0;process(
);}}}catch(IOException ex){}catch(AccessControlException ex){}if(!done){try(PrintWriter
pw0=select_output();){sc=new Scanner(System.in);pw=pw0;process();}}}private PrintWriter
select_output()throws FileNotFoundException{if(nameOut !=null){return new PrintWriter
(nameOut);}return new PrintWriter(System.out);}}
//end net/leksi/contest/Solver.java
}
