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:
/*                 _____                                                             ___
    /\      /\    |     | |   |    /\       /\      /\       /\      /\       /\    |   \     محمد أبوحسن*
   /  \    /  \   |     | |___|   /__\     /  \    /  \     /  \    /  \     /__\   |    \
  /    \  /    \  |     | |   |  /    \   /    \  /    \   /    \  /    \   /    \  |    /
 /      \/      \ |_____| |   | /      \ /      \/      \ /      \/      \ /      \ |___/
 */
import java.util.*;
public class Mohammad {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int t = sc.nextInt();
        while (t-- > 0) {
            long n = sc.nextLong();
            long k = sc.nextLong();
            if (n >= k && (n-k)%2 == 0) {
                System.out.println("YES");
                System.out.print((n - k + 1) + " ");
                for (int i = 1; i < k; i++) 
                    System.out.print(1 + " ");
                System.out.println();
            }
            else if (n >= k*2 && n%2 == 0) {
                System.out.println("YES");
                System.out.print(((n+2)-k*2) + " ");
                for (int i = 1; i < k; i++)
                    System.out.print(2 + " ");
                System.out.println();
            }
            else
                System.out.println("NO");
        }
    }
}