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.ArrayList;
import java.util.List;
import java.util.StringTokenizer;

public class Main {
    public static InputReader in = new InputReader(System.in);
    public static PrintWriter out = new PrintWriter(new OutputStreamWriter(System.out));

    public static void main(String[] args) {
        TaskB solver = new TaskB();
        TaskB.solve(1, in, out);
        out.flush();
        out.close();
    }

    static class TaskB {
        public static void solve(int testNumber, InputReader in, PrintWriter out) {
            int t = in.nextInt();
            for (int i = 0; i < t; i++) {
                int n = in.nextInt();
                int k = in.nextInt();
                judgeGood(n, k);
            }
        }

        public static void judgeGood(int N, int K) {
            if (K % 2 == 0 && N % 2 != 0) {
                out.println("NO");
                return;
            }
            List<Integer> solution = new ArrayList<>();
            boolean odd = K % 2 == 0 || N % 2 != 0;
            int sum = 0;
            for (int k = 0; k < K - 1; k++) {
                solution.add(odd ? 1 : 2);
                sum += solution.get(solution.size() - 1);
            }
            if (N <= sum) {
                out.println("NO");
                return;
            }
            solution.add(N - sum);
            out.println("YES");
            for (int i = 0; i < solution.size(); i++) {
                if (i != solution.size() - 1) {
                    out.print(solution.get(i) + " ");
                } else {
                    out.println(solution.get(i));
                }
            }
        }

    }
}

class InputReader {
    private final static int BUF_SZ = 65536;
    BufferedReader in;
    StringTokenizer tokenizer;

    public InputReader(InputStream in) {
        super();
        this.in = new BufferedReader(new InputStreamReader(in), BUF_SZ);
        tokenizer = new StringTokenizer("");
    }

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

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

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