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.lang.*; 
import java.util.*; 
 
public class Main { 
static String[] arr=new String[2];
public static void main(String[] args){ 
    Scanner in = new Scanner(System.in); 
    int n=in.nextInt(); 
   
    for(int k=0;k<n;k++){
       int x=in.nextInt();
       int y=in.nextInt();
       if(y>x){
           System.out.println("NO");
           continue;
       }
        if(y==1){
           System.out.println("YES");
           System.out.println(x);
           continue;
       }
       
       String ans="";
       int temp=x-y+1;
       if(temp%2==1&&temp>0){
           for(int j=0;j<y-1;j++){
               ans+=" "+1;
           }
           ans=(x-y+1)+ans;
           System.out.println("YES");
       System.out.println(ans);
       continue;
       }
       
         temp=x-2*(y-1);
       if(temp%2==0&&temp>0){
           for(int j=0;j<y-1;j++){
               ans+=" "+2;
           }
           ans=temp+ans;
           System.out.println("YES");
       System.out.println(ans);
       continue;
       }
       
       
       System.out.println("NO");
            
        }
      // String ans=solve();
       
        
    }
   
    
    public static String solve(){
        String ans="";
        
        
        
        
        return ans;
    }
}