Problem: Nastia has 2 positive integers A and B. She defines that:

  * The integer is good if it is divisible by A ⋅ B; 
  * Otherwise, the integer is nearly good, if it is divisible by A. 



For example, if A = 6 and B = 4, the integers 24 and 72 are good, the integers 6, 660 and 12 are nearly good, the integers 16, 7 are neither good nor nearly good.

Find 3 different positive integers x, y, and z such that exactly one of them is good and the other 2 are nearly good, and x + y = z.

Input

The first line contains a single integer t (1 ≤ t ≤ 10 000) — the number of test cases.

The first line of each test case contains two integers A and B (1 ≤ A ≤ 10^6, 1 ≤ B ≤ 10^6) — numbers that Nastia has.

Output

For each test case print: 

  * "YES" and 3 different positive integers x, y, and z (1 ≤ x, y, z ≤ 10^{18}) such that exactly one of them is good and the other 2 are nearly good, and x + y = z. 
  * "NO" if no answer exists. 

You can print each character of "YES" or "NO" in any case.

If there are multiple answers, print any.

Example

Input


3
5 3
13 2
7 11


Output


YES
10 50 60
YES
169 39 208
YES
28 154 182

Note

In the first test case: 60 — good number; 10 and 50 — nearly good numbers.

In the second test case: 208 — good number; 169 and 39 — nearly good numbers.

In the third test case: 154 — good number; 28 and 182 — nearly good numbers.

Solution (in JAVA):

Solution:
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.*;
import java.util.StringTokenizer;

public class code {
	static class FastReader {
		BufferedReader br;
		StringTokenizer st;

		public FastReader() {
			br = new BufferedReader(new
			                        InputStreamReader(System.in));
		}

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

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

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

		double nextDouble() {
			return Double.parseDouble(next());
		}

		String nextLine() {
			String str = "";
			try {
				str = br.readLine();
			} catch (IOException e) {
				e.printStackTrace();
			}
			return str;
		}
	};
	static long MOD=1000000007;
	public static void main(String[] args) {
		FastReader sc = new FastReader();
		PrintWriter pw = new PrintWriter(System.out);
		
		int t=sc.nextInt();
		while(t-->0){
			long a=sc.nextLong();
			long b=sc.nextLong();
			long x=a*b;
			if(b==1)
			{
				System.out.println("NO");
				continue;
			}
			System.out.println("YES");
			if(x-a==a || x-a<=0)
			{
				x=x*3;
			}

			System.out.println((a)+" "+(x-a)+" "+(x));
			
			
		}


		
		
		
		
		

	}
	static int dp[][];
	public static  boolean fn(int s,int e,int n,int m,int k,int cnt)
	{
		// System.out.println(s+" "+e+" "+cnt);
		if(s==n&&e==m){
			if(cnt==k)
				return true;
			return false;
		}
		if(s>n||e>m)
			return false;
		if(dp[s][e]!=-1)
		{
			if(dp[s][e]==1)
				return true;
			else
				return false;
		}
		boolean ans1=fn(s,e+1,n,m,k,cnt+s);
		// System.out.println(s+" "+e);
		boolean ans2=fn(s+1,e,n,m,k,cnt+e);
		 dp[s][e]=ans1||ans2==true?1:0;
		 return ans1||ans2;
	}
	
	

}