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.util.ArrayList;
import java.util.List;
import java.util.Scanner;

public class Solution {
    public static void main(String[] args) {
        Scanner scanner = new Scanner(System.in);
        int t = scanner.nextInt();

        for (int testCase = 0; testCase < t; testCase++) {
            int n = scanner.nextInt();
            int k = scanner.nextInt();

            List<String> output = new ArrayList<>();

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

            System.out.println(String.join(" ", output));
        }
    }
}


//101 k = 5;

//n gerade => take (k-1) * 2 + rest
//         => take (k-1) * 1 + rest if k == gerade

//n ungerade, k ungerade => take k * 1

//gerade ai => gerade
//ungerade ai, ki = gerade => gerade
//ungerade ai, ki = ungerade => ungerade