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.*;

public class Same_Parity_Summands {

	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		int t = sc.nextInt();
		
		for(int i = 0 ; i < t ; i++) {
			int[] x = new int[2];
			for(int j =0 ; j < 2 ; j++) {
				x[j] = sc.nextInt();
			}
			if(x[1] > x[0] || ( x[0]%2 == 1 & x[1] % 2 == 0)) {
				System.out.println("NO");
			}
			else if ( x[1] == x[0]) {
				System.out.println("YES");
				for(int j = 0; j < x[1]; j++) {
					System.out.print("1" + " ");
				}
				System.out.println("");
			}
			
			else if( x[1] <= x[0]/2 & x[0] %2 ==0) {
				System.out.println("YES");
				for(int j = 0; j < x[1]-1 ; j++) {
					System.out.print("2"+" ");
				}
				System.out.println(x[0]- 2*(x[1]-1));
			}
			else if(x[0] % 2 == 1 & x[1] % 2 == 1 || x[0] % 2 == 0 & x[1] % 2 == 0 ) {
				System.out.println("YES");
				for(int j =0 ; j < x[1]-1;j++) {
					System.out.print("1"+" ");
				}
				System.out.println( x[0]-(x[1]-1));
			}
			else System.out.println("NO");
			
			
		}

	}

}