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.*;
public class Problem1352b {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int t = sc.nextInt();
        while(t-->0) {
            int n = sc.nextInt();
            int k = sc.nextInt();
            boolean even = even(n, k);
            if(even == false) {
                boolean odd = odd(n, k);
                if(odd == false) {
                    System.out.println("NO");
                }
            }
        }
    }
    public static boolean even(int n, int k) {
        if((n - (k-1)*2) >= 2 && ((n - (k-1)*2)) %2 == 0) {
            System.out.println("YES");
            for(int i = 0; i < k-1; i++) {
                System.out.print(2 + " ");
            }
            System.out.println(n-(k-1)*2 + " ");
        }
        if((n - (k-1)*2) >= 2 && (n - (k-1)*2) %2 == 0) {
            return true;
        }
        return false;
    }
    public static boolean odd(int n, int k) {
        if(n-(k-1) >= 1 && ((n-(k-1))%2 == 1)) {
            System.out.println("YES");
            for(int i = 0; i < k-1; i++) {
                System.out.print(1 + " ");
            }
            System.out.println(n-(k-1));
        }
        if(n-(k-1) >= 1 && ((n-(k-1))%2 == 1)) {
            return true;
        }
        return false;
    }
}