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.Arrays;
import java.util.Scanner;

public class b {
	
	static int n, k;
	
	static int[] tryOne(int parity) {
		int[] nums = new int[k];
		int split = n / k;
		if (split % 2 != parity) {
			split--;
		}
		int leftover = n - split * k;
		for (int i = 0; i < k; ++i) {
			nums[i] = split;
		}
		for (int i = 0; leftover > 0 && i < k; ++i) {
			if (leftover >= 2) {
				nums[i] += 2;
				leftover -= 2;
			}
		}
		for (int i = 0; leftover > 0 && i < k; ++i) {
			int add = leftover;
			if (add % 2 != 0) {
				add--;
			}
			nums[i] += add;
			leftover -= add;
		}
		for (int i = 0; i < k; ++i) {
			if (nums[i] < 1) {
				leftover = 1;
				break;
			}
		}
		if (leftover > 0) {
			return null;
		}
		return nums;
	}

	public static void main(String[] args) {
		Scanner scan = new Scanner(System.in);
		for (int tt = scan.nextInt(), t = 1; t<= tt; ++t) {
			n = scan.nextInt();
			k = scan.nextInt();
			// 1 + 1 = 2
			// 2 + 2 = 4
			int[] nums1 = tryOne(1);
			if (nums1 == null) {
				nums1 = tryOne(0);
			}
//			System.out.print(t + " ");
			if (nums1 == null) {
				System.out.println("NO");
				continue;
			}
			System.out.println("YES");
			StringBuilder b = new StringBuilder();
			for (int i : nums1) {
				b.append(" ");
				b.append(i);
			}
			System.out.println(b.substring(1));
		}
	}

}