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.StringTokenizer;
import java.io.IOException;
import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.io.InputStream;

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

    static class BSameParitySummands {
        public void solve(int testNumber, FastReader in, PrintWriter out) {
            int t = in.nextInt();
            while (t-- > 0) {
                long n = in.nextLong();
                long k = in.nextLong();
                if (n < k) {
                    out.println("NO");
                } else if ((n - k + 1) > 0 && (n - k + 1) % 2 == 1) {
                    out.println("YES");
                    for (int i = 1; i <= k - 1; i++) {
                        out.print(1 + " ");
                    }
                    out.print((n - k + 1));
                    out.println();

                } else if ((n - (k - 1) * 2) > 0 && (n - (k - 1) * 2) % 2 == 0) {
                    out.println("YES");
                    for (int i = 1; i <= k - 1; i++) {
                        out.print(2 + " ");
                    }
                    out.print((n - (k - 1) * 2));
                    out.println();
                } else {
                    out.println("NO");
                }
            }
        }

    }

    static class FastReader {
        BufferedReader br;
        StringTokenizer st;

        public FastReader(InputStream inputStream) {
            br = new BufferedReader(new
                    InputStreamReader(inputStream));
        }

        String next() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

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

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

    }
}