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 {
	static StreamTokenizer s = new StreamTokenizer(new BufferedReader(new InputStreamReader(System.in)));
    public static void main(String[] args) throws IOException {
		var out = new PrintWriter(System.out);
		var sc = new Scanner(System.in);
		int t = nextInt();
		for (; t>0; t--) {
			int n = nextInt();
			int k = nextInt();
			int m = 1;
			int[] ans = new int[k];
			boolean no = false;
			if (n%2 == 1 && k%2 == 0) no = true;
			else if (n%2 == 0 && k%2 == 1) m = 2;
			for (int i = 0; i < k-1; i++) ans[i] = m;
			ans[k-1] = n-k*m+m;
			if (ans[k-1] < m) no = true;
			if (no) out.println("NO");
			else {
				out.print("YES\n" + ans[0]);
				for (int i = 1; i < k; i++) out.print(" " + ans[i]);
				out.println();
			}
		}
		out.flush();
	}
	static int nextInt() throws IOException {
		s.nextToken();
		return (int)s.nval;
	}
}