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:
/* package codechef; // don't place package name! */

import java.util.*;
import java.lang.*;
import java.io.*;
import java.util.Arrays;

/* Name of the class has to be "Main" only if the class is public. */
public class Main
{
	public static void main (String[] args) throws java.lang.Exception
	{
	     Scanner in=new Scanner(System.in);
	     int t,n,i,j,s=0,p,h,k;
	     String st="";
	     t=in.nextInt();
	     for(i=0;i<t;i++)
	     {
	          n=in.nextInt();
	          k=in.nextInt();
	          p=(n-k+1);
	          h=(n-(k-1)*2);
	          if(p%2!=0 && p>0)
	          {
	               System.out.println("YES");
	               for(j=0;j<k-1;j++)
	                    System.out.print("1 ");
	               System.out.println(p+" ");
	          }
	          else if(h%2==0 && h>0)
	          {
	               System.out.println("YES");
	               for(j=0;j<k-1;j++)
	                    System.out.print("2 ");
	               System.out.println(h+" ");
	          }
	          else 
	               System.out.println("NO");
	     }
	}
}