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.math.*;
import java.text.*;
import java.util.*;
 
public class sep2 {

   public static void main(String[] args) throws IOException {
    
        Scanner sc=new Scanner(System.in);
        int t=0;
        if(sc.hasNext())
         t=sc.nextInt();
        while(t>0)
        {
            int n=sc.nextInt();
            int k=sc.nextInt();
            ans(n,k);
            t--;
        }
    }
    public static void ans(int n,int k)
    {
        StringBuffer sbe=new StringBuffer();
        StringBuffer sbo=new StringBuffer();
        
        int en=n;
        int on=n;
        long se=0;
        int tk=k;
        long so=0;
        while(en>0&&k>0)
        {
            int d=(en/k+1)%2==0?en/k+1:en/k;
            k--;
            en-=d;
            sbe.append(d+" ");
            se+=d;
        }
        //k=(int)tk;
        while(on>0&&tk>0)
        {
            int d=(on/tk+1)%2!=0?on/tk+1:on/tk;
            tk--;
            on-=d;
            sbo.append(d+" ");
            
            so+=d;
        }
        if((so==n&&tk==0)||(se==n&&k==0))
        {
            System.out.println("YES");
        if((so==n&&tk==0))
        {
            System.out.println(sbo.toString());
         }
         else
         {
             System.out.println(sbe.toString());
            }
        }
        else
        {
            // System.out.println(sbe.toString());
            
            System.out.println("NO");
          //System.out.println(sbo.toString());
         
        }
       // System.out.println(ans);
        //System.out.println(sb.toString());
        
    }
}