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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.Comparator;
import java.util.List;
import java.util.StringTokenizer;

public class SameParitySummands { // Template for CF
    public static class ListComparator implements Comparator<List<Integer>> {

        @Override
        public int compare(List<Integer> l1, List<Integer> l2) {
            for (int i = 0; i < l1.size(); ++i) {
                if (l1.get(i).compareTo(l2.get(i)) != 0) {
                    return l1.get(i).compareTo(l2.get(i));
                }
            }
            return 0;
        }
    }

    public static void main(String[] args) throws IOException {
        // Check for int overflow!!!!
        // Should you use a long to store the sum or smthn?
        BufferedReader f = new BufferedReader(new InputStreamReader(System.in));
        PrintWriter out = new PrintWriter(System.out);

        int T = Integer.parseInt(f.readLine());
        for (int i = 0; i < T; i++) {
            StringTokenizer st = new StringTokenizer(f.readLine());
            int N = Integer.parseInt(st.nextToken());
            int k = Integer.parseInt(st.nextToken());
            if (N % 2 == 0) {
                if (k % 2 == 0) {
                    if (N >= k) {
                        out.println("YES");
                        for (int j = 0; j < k - 1; j++) {
                            out.print(1 + " ");
                            N--;
                        }
                        out.print(N);
                        out.println();
                    } else {
                        out.println("NO");
                    }
                } else {
                    if (N >= k * 2) {
                        out.println("YES");
                        for (int j = 0; j < k - 1; j++) {
                            out.print(2 + " ");
                            N -= 2;
                        }
                        out.print(N);
                        out.println();
                    } else {
                        out.println("NO");
                    }
                }
            } else {
                if (k % 2 != 0) {
                    if (N >= k) {
                        out.println("YES");
                        for (int j = 0; j < k - 1; j++) {
                            out.print(1 + " ");
                            N--;
                        }
                        out.print(N);
                        out.println();
                    } else {
                        out.println("NO");
                    }
                } else {
                    out.println("NO");
                }
            }
        }
        out.close();
    }

}