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.ArrayList;
import java.util.List;
import java.util.Scanner;

public class Main {

    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int tests = sc.nextInt();
        for (int z=0;z<tests;z++){
            int m;
            m = sc.nextInt();
            int k = sc.nextInt();
            if (k>m || (k%2==0 && m%2==1)){
                System.out.println("NO");
                continue;
            }
            if (m%2==1 && k%2==1){
                System.out.println("YES");
                for (int i=0;i<k-1;i++){
                    System.out.print(1 + " ");
                }
                System.out.println(m-k+1);
            }
            else if (m%2==0 && k%2==0){

                System.out.println("YES");
                for (int i=0;i<k-1;i++){
                    System.out.print(1 + " ");
                }
                System.out.println(m-k+1);
            }
            else{
                if ((k-1)*2 >=m){
                    System.out.println("NO");
                    continue;
                }
                System.out.println("YES");
                for (int i=0;i<k-1;i++){
                    System.out.print(2 + " ");
                }
                System.out.println(m - 2*(k-1));
            }
        }

    }
}