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 B {
    public static void main(String[] args) {
        try (Scanner s = new Scanner(System.in)) {
            final int t = s.nextInt();
            for (int i = 0; i < t; i++) {
                final int n = s.nextInt();
                final int k = s.nextInt();
                if (k > n) {
                    System.out.println("NO");
                } else {
                    if ((n - k + 1) % 2 == 1) {
                        System.out.println("YES");
                        for (int j = 0; j < k - 1; j++) {
                            System.out.print("1 ");
                        }
                        System.out.println(n - k + 1);
                    } else if (n % 2 == 0 && 2 * (k - 1) <= n - 2) {
                        System.out.println("YES");
                        for (int j = 0; j < k - 1; j++) {
                            System.out.print("2 ");
                        }
                        System.out.println(n - 2 * (k - 1));
                    } else {
                        System.out.println("NO");
                    }
                }
            }
        }
    }
}