Problem: You are given two positive integers n (1 ≤ n ≤ 10^9) and k (1 ≤ k ≤ 100). Represent the number n as the sum of k positive integers of the same parity (have the same remainder when divided by 2).

In other words, find a_1, a_2, …, a_k such that all a_i>0, n = a_1 + a_2 + … + a_k and either all a_i are even or all a_i are odd at the same time.

If such a representation does not exist, then report it.

Input

The first line contains an integer t (1 ≤ t ≤ 1000) — the number of test cases in the input. Next, t test cases are given, one per line.

Each test case is two positive integers n (1 ≤ n ≤ 10^9) and k (1 ≤ k ≤ 100).

Output

For each test case print:

  * YES and the required values a_i, if the answer exists (if there are several answers, print any of them); 
  * NO if the answer does not exist. 



The letters in the words YES and NO can be printed in any case.

Example

Input


8
10 3
100 4
8 7
97 2
8 8
3 10
5 3
1000000000 9


Output


YES
4 2 4
YES
55 5 5 35
NO
NO
YES
1 1 1 1 1 1 1 1
NO
YES
3 1 1
YES
111111110 111111110 111111110 111111110 111111110 111111110 111111110 111111110 111111120

Solution (in JAVA):

Solution:
import java.io.*;
import java.util.*;
public class Main1
{

	

	public static void main(String args[])throws IOException
	{
		BufferedReader br= new BufferedReader(new InputStreamReader(System.in));
		int t = Integer.parseInt(br.readLine());
		while(t-->0)
		{

			StringTokenizer st = new StringTokenizer(br.readLine());
			int n =Integer.parseInt(st.nextToken());
			int k = Integer.parseInt(st.nextToken());
			if(n%k==0)
			{System.out.println("YES");
				for(int i=0;i<k;i++)
					System.out.print(n/k+" ");
			System.out.println();
			continue;
			}
			int x = n/k;
			if(x>0){
			int r = n-(k-1)*x;
			if((x%2==0&&r%2==0)||(x%2!=0&&r%2!=0)){
				System.out.println("YES");
				for(int i=1;i<k;i++)
					System.out.print(x+" ");
				System.out.print(r);
				System.out.println();
				continue;
				}
			
			else{
				x--;
				if(x>0){
				  r=n-(k-1)*x;
				if((x%2==0&&r%2==0)||(x%2!=0&&r%2!=0)){
				System.out.println("YES");
				for(int i=1;i<k;i++)
					System.out.print(x+" ");
				System.out.print(r);
				System.out.println();
				continue;
			}}

			}}
			System.out.println("NO");


				
			
			
			

		}
	}


	}