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 MyClass {
    public static void main(String args[]) {
      Scanner sc = new Scanner(System.in);
      int t = sc.nextInt();
      while(t-->0)
      {
          long n = sc.nextLong();
          long k = sc.nextInt();
          ArrayList<Long> arr = new ArrayList<Long>();
          if((n%2==(k*2)%2&&n>=k*2))
          {
              System.out.println("YES");
              for(int i=0;i<k-1;i++)
              {
                  System.out.print(2+" ");
                  n=n-2;
              }
              System.out.println(n);
              
          }
          else if((n%2==(k*3)%2&&n>=k))
          {
              System.out.println("YES");
              for(int i=0;i<k-1;i++)
              {
                  System.out.print(1+" ");
                  n=n-1;
              }
              System.out.println(n);
          }
          else
          {
              System.out.println("NO");
          }
      }
          
    }
}