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.FileNotFoundException;
import java.util.ArrayList;
import java.util.List;
import java.util.Scanner;

public class HackerRank {

	public static void main(String[] args) throws FileNotFoundException {
		// Scanner sc = new Scanner(new File("src\\input.txt"));
		Scanner sc = new Scanner(System.in);

		int t = sc.nextInt();

		while (t-- != 0) {
			int n = sc.nextInt(), k = sc.nextInt();

			if ((n % 2 != 0 && k % 2 == 0)) {
				System.out.println("NO");
			} else if (n < k) {
				System.out.println("NO");
			} else {
				if (n % k == 0) {
					System.out.println("YES");
					for (int i = 0; i < k; i++) {
						if (i == 0) {
							System.out.print(n / k);
						} else {
							System.out.print(" " + n / k);
						}
					}
					System.out.println("");
				} else if (n % 2 == 0 && k % 2 != 0) {
					if (k > n / 2) {
						System.out.println("NO");
					} else {
						System.out.println("YES");
						for (int i = 0; i < k; i++) {
							if (i == 0) {
								System.out.print(n - 2 * (k - 1));
							} else {
								System.out.print(" " + 2);
							}
						}
						System.out.println("");
					}
				} else {
					System.out.println("YES");
					for (int i = 0; i < k; i++) {
						if (i == 0) {
							System.out.print(n - (k - 1));
						} else {
							System.out.print(" " + 1);
						}
					}
					System.out.println("");
				}
			}

		}
	}

}

/*
 * class Paire { int a; int b;
 * 
 * public Paire(int a, int b) { this.a = a; this.b = b; } }
 */