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.*;
import java.util.*;

public class Contest640B
{
	static class InputReader {
		BufferedReader reader;
		StringTokenizer tokenizer;
		public InputReader(InputStream stream) {
			reader = new BufferedReader(new InputStreamReader(stream), 32768);
			tokenizer = null;
		}
		String next() { // reads in the next string
			while (tokenizer == null || !tokenizer.hasMoreTokens()) {
				try {
					tokenizer = new StringTokenizer(reader.readLine());
				} catch (IOException e) {
					throw new RuntimeException(e);
				}
			}
			return tokenizer.nextToken();
		}
		public int nextInt() { // reads in the next int
			return Integer.parseInt(next());
		}
		public long nextLong() { // reads in the next long
			return Long.parseLong(next());
		}
		public double nextDouble() { // reads in the next double
			return Double.parseDouble(next());
			}
		}
	static InputReader r = new InputReader(System.in);
	static PrintWriter pw = new PrintWriter(System.out);
	public static void main(String[] args)
	{
		int t = r.nextInt();
		for (int t1 = 0; t1 < t; t1 ++)
		{
			int n = r.nextInt();
			int k = r.nextInt();
			if ((n%2 == 1) && (k%2 == 0))
			{
				pw.println("NO");
			}
			else if (n%2 == 1)
			{
				if (n < k)
				{
					pw.println("NO");
					continue;
				}
				else
				{
					pw.println("YES");
					for (int i = 0; i < k - 1; i ++)
					{
						pw.println(1);
					}
					pw.println(n-k+1);
				}
			}
			else if (k%2 == 0)
			{
				if (n < k)
				{
					pw.println("NO");
					continue;
				}
				else
				{
					pw.println("YES");
					for (int i = 0; i < k - 1; i ++)
					{
						pw.println(1);
					}
					pw.println(n-k + 1);
				}
			}
			else
			{
				if (n < 2*k)
				{
					pw.println("NO");
					continue;
				}
				else
				{
					pw.println("YES");
					for (int i =0 ; i < k - 1; i ++)
					{
						pw.println(2);
					}
					pw.println(n-2*(k-1));
				}
			}
		}
		
		pw.close();
	}
}