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.util.*;

public class Solution {

    public void solve() {
        for (int test = reader.nextInt(); test > 0; test--) {
            int n = reader.nextInt();
            int k = reader.nextInt();
            int[] a = find(n, k);
            if (a == null) {
                writer.println("NO");
            } else {
                writer.println("YES");
                for (int i = 0; i < k; i++) writer.print(a[i] + " ");
                writer.println();
            }
        }
    }

    int[] find(int n, int k) {
        int[] a = new int[k];
        a[k-1] = n;

        if (n % 2 == 0 && k % 2 == 1) {
            for (int i = 0; i < k-1; i++) {
                a[i] = 2;
                a[k-1] -= a[i];
            }
        } else {
            for (int i = 0; i < k-1; i++) {
                a[i] = 1;
                a[k-1] -= a[i];
            }
        }

        if (a[k-1] <= 0 || a[k-1] % 2 != a[0] % 2) return null;
        return a;
    }

    private InputReader reader;
    private PrintWriter writer;

    public Solution(InputReader reader, PrintWriter writer) {
        this.reader = reader;
        this.writer = writer;
    }

    public static void main(String[] args) {
        InputReader reader = new InputReader(System.in);
        PrintWriter writer = new PrintWriter(System.out);

        Solution solution = new Solution(reader, writer);
        solution.solve();

        writer.flush();
    }

    static class InputReader {
        private static final int BUFFER_SIZE = 1 << 20;

        private BufferedReader reader;
        private StringTokenizer tokenizer;

        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream), BUFFER_SIZE);
            tokenizer = null;
        }

        public String nextToken() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException();
                }
            }
            return tokenizer.nextToken();
        }

        public int nextInt() {
            return Integer.parseInt(nextToken());
        }

        public long nextLong() {
            return Long.parseLong(nextToken());
        }
    }
}