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.Scanner;

public class TRen3 {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int t = sc.nextInt();
        for (int cas = 0; cas < t; cas++) {
           int n = sc.nextInt();
            int k = sc.nextInt();
            if (n % k == 0) {
                System.out.println("YES");
                for (int i = 0; i < k; i++) {
                    System.out.print((n/k) + " ");
                }
                System.out.println(" ");
            }else {
                if (n % 2 == 1 && k % 2 == 0) {
                    System.out.println("NO");
                }else {
                    if (n < k) {
                        System.out.println("NO");
                    }else {
                        if ((n % k) % 2 == 0) {
                            System.out.println("YES");
                            System.out.print((n / k + (n % k)) + " ");
                            for (int i = 0; i < k - 1; i++) {
                                System.out.print((n / k) + " ");
                            }
                            System.out.println(" ");
                        } else {
                            if ((n % 2 == 0 && k % 2 == 1) && k * 2 <= n) {
                                System.out.println("YES");
                                System.out.print(((n - k * 2) + 2) + " ");
                                for (int i = 0; i < k - 1; i++) {
                                    System.out.print(2 + " ");
                                }
                            } else {
                                if ((n % 2 == 0 && k % 2 == 1) && k * 2 > n){
                                    System.out.println("NO");
                                }else {
                                    if (n % 2 == 0 && k % 2 == 0) {
                                        System.out.println("YES");
                                        System.out.print((n - k + 1) + " ");
                                        for (int i = 0; i < k - 1; i++) {
                                            System.out.println(1 + " ");
                                        }
                                    } else {
                                        if (n % 2 == 1 && k % 2 == 1) {
                                            System.out.println("YES");
                                            System.out.print((n - k + 1) + " ");
                                            for (int i = 0; i < k - 1; i++) {
                                                System.out.println(1 + " ");
                                            }
                                        }
                                    }
                                }
                            }
                        }
                    }
                }
            }
        }
    }
}