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.InputStreamReader;
import java.util.Arrays;
import java.util.Scanner;

public class Solution1352B {

    public static void main(String[] args) {
        Scanner in = new Scanner(new BufferedReader(new InputStreamReader(System.in)));
        int T = in.nextInt();

        while (T-- > 0) {
            int n = in.nextInt();
            int m = in.nextInt();

            solve(n, m);
        }
    }

    private static void solve(int n, int m) {
        //System.out.println(n + " " + m + " ==== ");

        if (m > n) {
            System.out.println("NO");
            return;
        }


        var a = n - (m - 1);
        var b = n - (m - 1) * 2;
        if (a % 2 == 1 && a > 0) {
            System.out.println("YES");
            System.out.println("1 ".repeat(m - 1) + a);
            return;
        } else if (b > 0 && b % 2 == 0) {
            System.out.println("YES");
            System.out.println("2 ".repeat(m - 1) + b);
            return;
        }

        System.out.println("NO");



    }

    static int[] toArray(String str) {
        return Arrays.stream(str.split(" ")).mapToInt(Integer::valueOf).toArray();
    }
}