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 Solution {
    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();
            if(k <= n){
                if(n%2 == 0 && k%2==1 && k>n/2){
                    System.out.print("NO");
                }else if(n%2==1 && k%2==0){
                    System.out.print("NO");
                }else{
                    int val1 = n - (k-1);
                    int val2 = n - 2*(k-1);
                    if((val1%2==1 && val1 > 0)|| (val2%2==0 && val2>0)){
                        System.out.println("YES");
                        if(val1%2==1){
                            for(int i=0;i<k-1;i++){
                                System.out.print(1 + " ");
                            }
                            System.out.print(val1);
                        }else{
                            for(int i=0;i<k-1;i++){
                                System.out.print(2 + " ");
                            }
                            System.out.print(val2);
                        }
                    }else{
                        System.out.print("NO");
                    }
                }
            }else{
                System.out.print("NO");
            }
            System.out.println();
            t--;
        }
    }
}