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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.StringTokenizer;

public class Q1352bsameparitysummands 
{
	public static void main(String[] Arguments) throws IOException 
	{
		BufferedReader BR = new BufferedReader(new InputStreamReader(System.in));
		int t = Integer.parseInt(BR.readLine());
		for (; t > 0; t--)
		{
			StringTokenizer ST = new StringTokenizer(BR.readLine());
			int n = Integer.parseInt(ST.nextToken()), k = Integer.parseInt(ST.nextToken());
			int n1 = n - (k - 1);
			if (n1 > 0 && n1 % 2 == 1)
			{
				System.out.println("YES");
				for (int i = 0; i < k - 1; i++) System.out.print("1 ");
				System.out.println(n1);
				continue;
			}
			
			int n2 = n - 2 * (k - 1);
			if (n2 > 0 && n2 % 2 == 0)
			{
				System.out.println("YES");
				for (int i = 0; i < k - 1; i++) System.out.print("2 ");
				System.out.println(n2);
				continue;
			}
			System.out.println("NO");
		}
	}
}