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.ArrayList;
import java.util.List;
import java.util.Scanner;
import java.util.stream.Collectors;

public class Contest2 {

    public static void main(String[] args) {
        Scanner s = new Scanner(System.in);
        int tc = Integer.parseInt(s.nextLine());

        for (int i = 0; i < tc; ++i) {
            String c = s.nextLine();
            String[] parts = c.split(" ");

            long n = Long.parseLong(parts[0].trim());
            long m = Long.parseLong(parts[1].trim());
            solve(n, m);
        }
    }

    private static void solve(long n, long m) {
        long val = n / m;
        long sum = val * m;
        if (sum == n) {
            System.out.println("YES");
            for (int i = 0; i < m; ++i) {
                String s = " ";
                if (i + 1 == m) s = "";
                System.out.print(val + s);
            }
            System.out.println();
        }
        else if (sum <= 0) {
            System.out.println("NO");
        }
        else {
            long rest = n - sum;
            long last = val + rest;
            boolean leven = last % 2 == 0;
            boolean veven = val % 2 == 0;
            if (leven ^ veven) {
                if ((m - 1) % 2 != 0 || (val - 1) <= 0) {
                    System.out.println("NO");
                } else {
                    System.out.println("YES");
                    for (int i = 0; i < m - 2; ++i) {
                        System.out.print((val-1) + " ");
                    }
                    System.out.print((val + (m-2)) + " ");
                    System.out.println(last);
                }
            } else {
                System.out.println("YES");
                for (int i = 0; i < m - 1; ++i) {
                    System.out.print(val + " ");
                }
                System.out.println(last);
            }
        }
    }

}