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.util.Scanner;
public class Main
{
	public static void main(String[] args) {
		Scanner sc=new Scanner(System.in);
		int t=sc.nextInt();
		while(t!=0)
		{
		    t--;
		    int x;
		    int y;
		    int n=sc.nextInt();
		    int k=sc.nextInt();
		    //for odd
		    x=k-1;
		    y=n-x;
		    if(y<=0)
		    {
		        System.out.println("NO");
		    }
		    else
		    {
    		    if(y%2==1)
    		    {
    		        System.out.println("YES");
    		        for(int i=0;i<k-1;i++)
    		        {
    		        System.out.print("1"+" ");
    		        }
    		        System.out.println(y);
    		    }
    		    else
    		    {
    		        
    		        x=2*x;
    		        y=n-x;
    		        
    		        if((y<=0)||(y%2==1))
        		    {
        		        System.out.println("NO");
        		    }
        		    else
        		    {
        		        System.out.println("YES");
        		        for(int i=0;i<k-1;i++)
        		        {
        		        System.out.print("2"+" ");
        		        }
        		        System.out.println(y);
        		    }
    		        
    		    }
	    	}
		    
		}
	}
}