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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;

public class B1352 {
    public static void main(String[] args) throws IOException {
        new B1352().run();
    }

    private void run() throws IOException {
        BufferedReader reader = new BufferedReader(new InputStreamReader(System.in));

        int t = Integer.parseInt(reader.readLine());

        while(t-- > 0) {
            String s[] = reader.readLine().split(" ");

            int n = Integer.parseInt(s[0]);
            int k = Integer.parseInt(s[1]);

            boolean odd = false;

            int newNum = n - k+1;
            if(newNum >0 && newNum%2==1){
                odd = true;
            }
            boolean even = false;
            if(!odd) {
                newNum = n - 2*(k-1);
                if(newNum >0 && newNum %2==0) {
                    even = true;
                }
            }

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

        }

    }
}