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.*;
import java.io.*;

public class main{

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