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.LinkedList;
import java.util.List;
import java.util.Scanner;

public class Solution {

    private static String solve(final int n, final int k, final List<String> result) {
        if (k > n) return "NO";

        if ((n & 1) == 1) {
            if ((k & 1) == 0) return "NO";

            for (int i = k - 1; i > 0; i -= 1) result.add(String.valueOf(1));
            result.add(String.valueOf(n - (k - 1)));
        } else {
            if ((k & 1) == 0) {
                for (int i = k - 1; i > 0; i -= 1) result.add(String.valueOf(1));
                result.add(String.valueOf(n - (k - 1)));
            } else {
                if (n < k * 2) return "NO";

                for (int i = k - 1; i > 0; i -= 1) result.add(String.valueOf(2));
                result.add(String.valueOf(n - 2 * (k - 1)));
            }
        }

        return "YES";
    }

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

        final int T = in.nextInt();

        for (int t = 0; t < T; t += 1) {
            int n = in.nextInt();
            int k = in.nextInt();

            List<String> result = new LinkedList<>();
            String answer = solve(n, k, result);
            System.out.println(answer);

            if (answer.equals("YES")) System.out.println(String.join(" ", result));
        }
    }
}