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.io.*;

public class parity_sum
{
    public static void main(String args[]) throws IOException
    {
        BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
        String inp[];
        int n,k;
        int t = Integer.parseInt(in.readLine());
        String result[] = new String[t];
        for (int i=0; i<t; i++)
        {
            inp = in.readLine().split(" ");
            n = Integer.parseInt(inp[0]);
            k = Integer.parseInt(inp[1]);
            if (n<k)
                result[i] = "NO";
            else if (n%k == 0)
            {
                result[i] = "YES\n";
                for (int j=0; j<k; j++)
                    result[i] += n/k + " ";
            }
            else
            {
                if ((n%k)%2 == 0)
                {
                    result[i] = "YES\n" + (n/k+n%k) + " ";
                    for (int j=0; j<k-1; j++)
                        result[i] += n/k + " ";
                }
                else if ((k-(n%k))%2 == 0 && n/k!=1)
                {
                    result[i] = "YES\n";
                    for (int j=0; j<n%k; j++)
                        result[i] += (n/k+1) + " ";
                    for (int j=0; j<(k-(n%k))/2; j++)
                        result[i] += (n/k+1) + " " + (n/k-1) + " ";
                }
                else
                    result[i] = "NO";
            }
        }
        for (int i=0; i<t; i++)
            System.out.println(result[i]);
    }
}