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 Main {
    static Scanner scan = new Scanner(System.in);
    static String test(){
        int n = scan.nextInt();
        int k = scan.nextInt();

        StringBuilder ans = new StringBuilder("");
        int last = n - (k - 1) * 2;
        if((last & 1) == 0 && last > 0){
            ans.append("YES").append('\n');
            for(int i = 0; i < k - 1; i ++){
                ans.append('2').append(' ');
            }
            ans.append(last);
        }
        else{
            last = n - (k - 1);
            if((last & 1) == 1 && last > 0){
                ans.append("YES").append('\n');
                for(int i = 0; i < k - 1; i ++){
                    ans.append(1).append(' ');
                }
                ans.append(last);
            }
        }
        if(ans.length() == 0){
            ans.append("NO");
        }
        ans.append('\n');
        return ans.toString();
    }
    public static void main(String[] args) {
        int T = scan.nextInt();
        StringBuilder answer = new StringBuilder("");
        for(int tc = 0; tc < T; ++ tc){
             answer.append(test());
        }
        System.out.println(answer);
    }
}