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;

public class Solution {

	public static void main(String[] args) {
		final Scanner in = new Scanner(System.in);

		for (int z = in.nextInt(); z > 0; z--) {
			final int n = in.nextInt();
			final int k = in.nextInt();
			if (n < k || (n & 1) == 1 && (k & 1) == 0)
				System.out.println("NO");
			else {
				final int min = (k & 1) == 1 ? 2 - (n & 1) : 1;
				if (n - min * k < 0) {
					System.out.println("NO");
				} else {
					System.out.println("YES");
					for (int i = 1; i < k; i++) {
						System.out.print(min + " ");
					}
					System.out.println(n - min * k + min);
				}
			}
		}
	}
}