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 static java.lang.System.in;
import static java.lang.System.out;

public class B {

    public static void main(String[] args) {
        final Scanner scan = new Scanner(in);
        long t = scan.nextLong();
        while (t-- > 0) {
            long n = scan.nextLong();
            long k = scan.nextLong();
            if (n < k) {
                out.print("NO\n");
                continue;
            }
            long val = n / k;
            long rem = n % k;
            if (rem % 2 == 0) {
                out.print("YES\n");
                out.print(val + rem + " ");
                for (int i = 0; i < k - 1; i++) {
                    out.print(val + " ");
                }
            } else if (rem % 2 == 1 && k % 2 == 0) {
                out.print("NO");
            } else if (rem % 2 == 1 && k % 2 == 1) {
                if (val <= 1) {
                    out.print("NO");
                } else {
                    out.print("YES\n");
                    out.print(val + rem + " ");
                    for (int i = 0; i < k - 1; i++) {
                        if (i % 2 == 0) {
                            out.print(val - 1 + " ");
                        } else {
                            out.print(val + 1 + " ");
                        }
                    }
                }
            }
            out.print("\n");
        }
    }
}