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.math.BigInteger;
import java.util.*;

public class Main {

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

    }
}