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.*;

public class JavaApplication161 {

    /**
     * @param args the command line arguments
     */
    static class node{
        int x;
        int y;
        public node(int x, int y)
        {
            this.x=x;
            this.y=y;
        }
    }
    public static void main(String[] args) {
        // TODO code application logic here
        Scanner sc=new Scanner(System.in);
        int t=sc.nextInt();
       while(t--!=0)
       {
           int n=sc.nextInt();
           int k=sc.nextInt();
           if(k%2!=0 && n%2==0)
           {
                 if(n/k!=0)
                 {
                      int l=n-2*(k-1);
                      if(l>0){
                     System.out.println("YES");
                     for(int i=0;i<k-1;i++)
                     {
                         System.out.print("2 ");
                     }
                    
                     System.out.print(l);
                     System.out.println();
                 }
                      else
                          System.out.println("NO");
                 }
                 else
                     System.out.println("NO");
           }
           else if(k%2!=0 && n%2!=0)
           {
               if(n/k!=0)
               { 
                     int d=n-(k-1);
                     if(d>0){
                    System.out.println("YES");
                 
                   for(int i=0;i<k-1;i++)
                       System.out.print("1 ");
                    System.out.print(d);
                     System.out.println();
               }
                     else
                         System.out.println("NO");
               }
               else
                   System.out.println("NO");
           }
           else if(k%2==0 && n%2==0){
               if(n/k!=0)
               {
                      int d=n-(k-1);
                      if(d>0){
                 System.out.println("YES");   
               
                   for(int i=0;i<k-1;i++)
                       System.out.print("1 ");
                    System.out.print(d);
                     System.out.println(); 
               }
                      else
                                System.out.println("NO");
               }
                else
                   System.out.println("NO");
           
           }
           else
           {
               System.out.println("NO");
           }
       }
       
    }
    
}