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.*;
import java.math.*;
 
public class Main {

	private static FastReader fastReader = new FastReader();

	public static void main(String[] args) {
		Task solver = new Task();
		solver.solve();
	}

	static class Task {
		private static StringBuilder result = new StringBuilder();
		private static int[] arr = new int[10000002];

		private static void sieve(int[] arr) {
			for(int i=4; i<10000002; i+=2) arr[i] = 2;
			for(int i=3; i*i < 10000002; i+=2){
				if(arr[i] == 0){
					for(int j=i*i; j<10000002; j+= i){
						if(arr[j] == 0) arr[j] = i;
					}
				}
			}
		}

		public void solve() {
			int nt = fastReader.nextInt();
			sieve(arr);
			while (nt-- > 0) {
				int num = fastReader.nextInt();
				int k =fastReader.nextInt();
				num += arr[num] == 0 ? num : arr[num];
				long ans = num + (k-1)*2;
				result.append(ans+"\n");
			}
			System.out.println(result.toString());
		}
	}

	static class FastReader {
		public BufferedReader reader;
		public StringTokenizer tokenizer;
		private static PrintWriter pw;

		public FastReader() {
			reader = new BufferedReader(new InputStreamReader(System.in));
			pw = new PrintWriter(System.out);
			tokenizer = null;
		}

		public String next() {
			while (tokenizer == null || !tokenizer.hasMoreTokens()) {
				try {
					tokenizer = new StringTokenizer(reader.readLine());
				} catch (IOException e) {
					throw new RuntimeException(e);
				}
			}
			return tokenizer.nextToken();
		}

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

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

		public String readLine() {
			try {
				return reader.readLine();
			} catch (IOException e) {
				e.printStackTrace();
			}
			return null;
		}

		public static void print(String str) {
			pw.print(str);
			pw.flush();
		}
	}
}