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.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Scanner;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
public class Main
{
    public static void main(String[] args)
    {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        Scanner in = new Scanner(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        TaskB solver = new TaskB();
        solver.solve(1, in, out);
        out.close();
    }

    static class TaskB
    {
        public void solve(int testNumber, Scanner in, PrintWriter out)
        {
            int T = in.nextInt();
            while (T-- > 0)
            {
                solve(in, out);
            }
        }

        private void solve(Scanner in, PrintWriter out)
        {
            int N = in.nextInt();
            int K = in.nextInt();
            int nums[] = new int[K];
            nums[0] = N;
            for (int i = 1; i < K; i++)
            {
                nums[i] = 2;
                nums[0] -= 2;
            }
            if (sameParity(nums))
            {
                printParity(nums, out);
                return;
            }
            nums[0] = N;
            for (int i = 1; i < K; i++)
            {
                nums[i] = 1;
                nums[0] -= 1;
            }
            if (sameParity(nums))
            {
                printParity(nums, out);
                return;
            }
            out.println("NO");
        }

        private void printParity(int[] nums, PrintWriter out)
        {
            out.println("YES");
            for (int i = 0; i < nums.length; i++)
            {
                if (i == nums.length - 1)
                {
                    out.print(nums[i]);
                } else
                {
                    out.print(nums[i] + " ");
                }
            }
            out.println();
        }

        boolean sameParity(int nums[])
        {
            if (nums[0] <= 0) return false;
            for (int i = 1; i < nums.length; i++)
            {
                if ((nums[i] % 2) != (nums[0] % 2))
                {
                    return false;
                }
            }
            return true;
        }

    }
}