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:
//Created by Aminul on 5/9/2020.

import java.io.*;
import java.util.*;

import static java.lang.Math.*;

public class B {
    public static void main(String[] args) throws Exception {
        Scanner in = new Scanner(System.in);
        PrintWriter pw = new PrintWriter(System.out);
        int test = in.nextInt();
        for (int t = 1; t <= test; t++) {
            int n = in.nextInt(), k = in.nextInt();
            List<Integer> g = solve(n, k);
            if (g == null) pw.println("NO");
            else {
                pw.println("YES");
                for (int i : g) pw.print(i + " ");
                pw.println();
            }
        }

        pw.close();
    }

    static List<Integer> solve(int n, int k) {
        if (k > n) return null;
        List<Integer> g = null;
        if ((n - (k - 1)) > 0 && (n - (k - 1)) % 2 == 1) { // check odd
            g = new ArrayList<>();
            for (int i = 1; i <= k - 1; i++) {
                g.add(1);
            }
            g.add(n - (k - 1));
        } else if ((n - (k - 1) - (k - 1)) > 0 &&
                (n - (k - 1) - (k - 1)) % 2 == 0) { // check even
            g = new ArrayList<>();
            for (int i = 1; i <= k - 1; i++) {
                g.add(2);
            }
            g.add(n - (k - 1) - (k - 1));
        }
        return g;
    }

    static void debug(Object... obj) {
        System.err.println(Arrays.deepToString(obj));
    }
}