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.
//package Codeforces;
import java.util.*;
import java.io.*;
public class D
{
   static final int mod = (int) 1e9 + 7;
   static final int inf = (int) 1e9;
   static final long INF = (long) 1e18;
   public static void main(String[] args) throws IOException 
   {
		FastScanner fs = new FastScanner();
		PrintWriter out = new PrintWriter(System.out);
		int T=fs.nextInt();
		while(T-->0)
		{
			int n=fs.nextInt();int k=fs.nextInt();
			if(n%2==0)
			{
				long ans=n+(long)(k*2);
				System.out.println(ans);
			}
			else
			{
				int min=inf;
				for(int i=1;i<=Math.sqrt(n);i++)
				{
					if(n%i==0)
					{	if(i!=1)min=Math.min(min,i);
					min=Math.min(min,n/i);}
				}
				k--;
		      //  System.out.println(min);
				long ans=(n+min)+(long)(k*2);
				System.out.println(ans);
			}
		}
   }
	public static int upper_bound(int arr[],int key)
	{
		int index=inf,num=0;
		int left=0,right=arr.length-1;
		while(left<=right)
		{
			int mid=left+(right-left)/2;
			if(arr[mid]<=key) {index=mid;num=arr[mid];left=mid+1;}
			else 
				right=mid-1;
		}
		return index==inf ? arr.length:index;
	}
}
class FastScanner {
	BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
	StringTokenizer st = new StringTokenizer("");

	public String next() {
		while (!st.hasMoreTokens())
			try {
				st = new StringTokenizer(br.readLine());
			} catch (IOException e) {
				e.printStackTrace();
			}
		return st.nextToken();

	}

	public String nextLine() throws IOException {
		return br.readLine();
	}

	int[] sort(int arr[]) {
		ArrayList<Integer> list = new ArrayList<Integer>();
		for (int i : arr)
			list.add(i);
		Collections.sort(list);
		for (int i = 0; i < arr.length; i++) {
			arr[i] = list.get(i);
		}
		return arr;
	}

	char[] charsort(char arr[]) {
		ArrayList<Character> list = new ArrayList<>();
		for (char c : arr)
			list.add(c);
		Collections.sort(list);
		for (int i = 0; i < list.size(); i++) {
			arr[i] = list.get(i);
		}
		return arr;
	}

	long[] longsort(long arr[]) {
		ArrayList<Long> list = new ArrayList<Long>();
		for (long i : arr)
			list.add(i);
		Collections.sort(list);
		for (int i = 0; i < arr.length; i++) {
			arr[i] = list.get(i);
		}
		return arr;
	}

	public int nextInt() {
		return Integer.parseInt(next());
	}

	public int[] readArray(int n) {
		int[] arr = new int[n];
		for (int i = 0; i < n; i++)
			arr[i] = nextInt();
		return arr;
	}

	public long nextLong() {
		return Long.parseLong(next());
	}

	public long[] longreadArray(int n) {
		long[] a = new long[n];
		for (int i = 0; i < n; i++)
			a[i] = nextLong();
		return a;
	}
}
