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 B {
    Random random = new Random(751454315315L + System.currentTimeMillis());

    public void solve() throws IOException {
        int t = nextInt();
        while (t-- > 0) {
            int n = nextInt();
            int k = nextInt();
            if (k > n || k % 2 == 0 && n % 2 == 1) {
                out.println("NO");
                continue;
            }
            if (n % 2 == 1) {
                out.println("YES");
                for (int i = 0; i < k - 1; i ++) {
                    out.print(1 + " ");
                }
                out.println(n - k + 1);
            } else {
                if (k % 2 == 0) {
                    out.println("YES");
                    for (int i = 0; i < k - 1; i ++) {
                        out.print(1 + " ");
                    }
                    out.println(n - k + 1);
                } else {
                    if (n <= 2 * (k - 1)) {
                        out.println("NO");
                    } else {
                        out.println("YES");
                        for (int i = 0; i < k - 1; i ++) {
                            out.print(2 + " ");
                        }
                        out.println(n - 2 * k + 2);
                    }
                }
            }
        }
    }

    public void run() {
        try {
            br = new BufferedReader(new InputStreamReader(System.in));
            out = new PrintWriter(System.out);

            solve();

            out.close();
        } catch (IOException e) {
            e.printStackTrace();
            System.exit(1);
        }
    }

    private void shuffle(int[] s) {
        for (int i = 0; i < s.length; ++i) {
            int j = random.nextInt(i + 1);
            int t = s[i];
            s[i] = s[j];
            s[j] = t;
        }
    }

    class Pair implements Comparable<Pair> {
        int f;
        int s;

        public Pair(int f, int s) {
            this.f = f;
            this.s = s;
        }

        @Override
        public boolean equals(Object o) {
            if (this == o) return true;
            if (o == null || getClass() != o.getClass()) return false;
            Pair pair = (Pair) o;
            return f == pair.f &&
                    s == pair.s;
        }

        @Override
        public int hashCode() {
            return Objects.hash(f, s);
        }

        @Override
        public int compareTo(Pair o) {
            if (f == o.f) {
                return s - o.s;
            }
            return f - o.f;
        }
    }

    BufferedReader br;
    StringTokenizer in;
    PrintWriter out;

    public String nextToken() throws IOException {
        while (in == null || !in.hasMoreTokens()) {
            in = new StringTokenizer(br.readLine());
        }
        return in.nextToken();
    }

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

    public double nextDouble() throws IOException {
        return Double.parseDouble(nextToken());
    }

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

    public int[] nextArr(int n) throws IOException {
        int[] res = new int[n];
        for (int i = 0; i < n; i++) {
            res[i] = nextInt();
        }
        return res;
    }

    public static void main(String[] args) throws IOException {
        Locale.setDefault(Locale.US);
        new B().run();
    }
}