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.Scanner;
import java.util.Vector;

public class Solution {
   

    public static void main(String[] args) {
   
       Scanner sc = new Scanner(System.in);
       int t=sc.nextInt();
       int k=0;
       while(k++<t) {
            
           int a=sc.nextInt();
           int b=sc.nextInt();
           int no=b;
           if((a-(b-1))%2!=0 && (a-(b-1)*1)>0) {
            System.out.println("YES");
            while(no-1>0) {
               
                System.out.print(1+" ");
                no--;
            }
            System.out.print(a-(b-1)*1);
            System.out.println("");
          
            continue;
        }
        else if((a-(b-1)*2)%2==0  && (a-(b-1)*2)>0) {
            System.out.println("YES");
            while(no-1>0) {
                System.out.print(2+" ");
                no--;
            }
            System.out.print(a-(b-1)*2);
            System.out.println("");
           
            continue;
        }
          
        System.out.println("NO");
         
        
           
       }
      
    }

}