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.
// coded by Krishna Sundar //

import java.lang.*;
import java.io.*;
import java.util.*;

public class Main {

    public void solve(Read input, Write output) throws Exception {
        int cases = input.readInt();
        while (cases-->0) {
            long N = input.readLong();
            long K = input.readLong();
            if (N%2l==0l) {
                output.printLine(""+(N+(2*K)));
            } else {
                int prime = 1;
                for (long i=2;(i*i)<=N;i++) {
                    if (N%i==0l) {
                        prime = 0;
                        output.printLine(""+(N+(i)+((K-1)*2)));
                        break;
                    }
                }
                if (prime==1) {
                    output.printLine(""+(N+(N)+((K-1)*2)));
                }
            }
            output.flush();
        }
    }

    public static void main(String[] args) throws Exception {
        Read input = new Read();
        Write output = new Write();
        Main D = new Main();
        D.solve(input, output);
        output.flush();
        output.close();
    }

    // java fast io reader and writer
    // taken from various sources and customized

    static class Read {

        private byte[] buffer =new byte[10*1024];
        private int index;
        private InputStream input_stream;
        private int total;

        public Read() {
            input_stream = System.in;
        }

        public int read()throws IOException {
            if(total<0)
                throw new InputMismatchException();
            if(index>=total) {
                index=0;
                total= input_stream.read(buffer);
                if(total<=0)
                    return -1;
            }
            return buffer[index++];
        }

        public long readLong() throws IOException {
            long number=0;
            int n= read();
            while(isWhiteSpace(n))
                n= read();
            long neg=1l;
            if(n=='-') {
                neg=-1l;
                n= read();
            }
            while(!isWhiteSpace(n)) {
                if(n>='0'&&n<='9') {
                    number*=10l;
                    number+=(long)(n-'0');
                    n= read();
                }
                else throw new InputMismatchException();
            }
            return neg*number;
        }

        public int readInt() throws IOException {
            int integer=0;
            int n= read();
            while(isWhiteSpace(n))
                n= read();
            int neg=1;
            if(n=='-') {
                neg=-1;
                n= read();
            }
            while(!isWhiteSpace(n)) {
                if(n>='0'&&n<='9') {
                    integer*=10;
                    integer+=n-'0';
                    n= read();
                }
                else throw new InputMismatchException();
            }
            return neg*integer;
        }

        public double readDouble()throws IOException {
            double doub=0;
            int n= read();
            while(isWhiteSpace(n))
                n= read();
            int neg=1;
            if(n=='-') {
                neg=-1;
                n= read();
            }
            while(!isWhiteSpace(n)&&n!='.') {
                if(n>='0'&&n<='9') {
                    doub*=10;
                    doub+=n-'0';
                    n= read();
                }
                else throw new InputMismatchException();
            }

            if(n=='.') {
                n= read();
                double temp=1;
                while(!isWhiteSpace(n)) {
                    if(n>='0'&&n<='9') {
                        temp/=10;
                        doub+=(n-'0')*temp;
                        n= read();
                    }
                    else throw new InputMismatchException();
                }
            }
            return doub*neg;
        }

        public String readString()throws IOException {
            StringBuilder sb = new StringBuilder();
            int n = read();
            while (isWhiteSpace(n))
                n = read();
            while (!isWhiteSpace(n)) {
                sb.append((char)n);
                n = read();
            }
            return sb.toString();
        }

        private boolean isWhiteSpace(int n) {
            if(n==' '|| n=='\n'|| n=='\r'|| n=='\t'|| n==-1)
                return true;
            return false;
        }
    }

    static class Write {

        private final BufferedWriter bw;

        public Write() {
            bw = new BufferedWriter(new OutputStreamWriter(System.out));
        }
        public void print(String str) throws IOException {
            bw.append(str);
        }
        public void printLine(String str) throws IOException {
            print(str);
            bw.append("\n");
        }
        public void close()throws IOException {
            bw.close();
        }
        public void flush()throws IOException {
            bw.flush();
        }
    }
}