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.*;
import java.io.*;
public class Main
{
    public static void main(String args[])throws Exception
    {
        BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
        
        PrintWriter pw=new PrintWriter(System.out);
        int t=Integer.parseInt(br.readLine());
        for(int x=0;x<t;x++)
        {
            String str[]=br.readLine().split(" ");
            int n=Integer.parseInt(str[0]);
            int k=Integer.parseInt(str[1]);
            if((n-(k-1)<=0||((n-(k-1)>0)&&(n-(k-1))%2==0))&&(n-2*(k-1)<=0||((n-2*(k-1)>0)&&(n-2*(k-1))%2!=0)))
            pw.println("NO");
            else if((n-(2*(k-1)))>0&&(n-(2*(k-1)))%2==0)
            {
                pw.println("YES");
                for(int i=0;i<k-1;i++)
                pw.print("2 ");
                pw.println((n-(2*(k-1))));
            }
            else
            {
                pw.println("YES");
                for(int i=0;i<k-1;i++)
                pw.print("1 ");
                pw.println((n-(k-1)));
            }
            //pw.println();
        }
        pw.flush();
        pw.close();
    }
}