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.Scanner;

public class SameParitySummands {
    public static void main(String[] args) {
        SameParitySummands obj = new SameParitySummands();
        Scanner s = new Scanner(System.in);
        int tests = s.nextInt();
        while (tests > 0) {
            int n = s.nextInt();
            int k = s.nextInt();
            if (n%2!=0 && k%2==0 || n < k) System.out.println("NO");
            else {
                ArrayList<Integer> summands = obj.sameParitySummands(n, k);
                if (summands.size() > 0) {
                    System.out.println("YES");
                    for (int summand: summands) {
                        System.out.print(summand);
                        System.out.print(" ");
                    }
                    System.out.println();
                }else {
                    System.out.println("NO");
                }
            }
            tests--;
        }
    }

    private ArrayList<Integer> sameParitySummands(int n, int k) {
        ArrayList<Integer> summands = new ArrayList<>();
        boolean evenParirtyPossible = false;
        if (n%2 == 0 && k%2!=0) {
            evenParirtyPossible = true;
            if (n - 2 * (k-1) < 0) {
                return summands;
            }
        }
        else {
            if ((n-k-1)%2==0) {
                return summands;
            }
        }
        if (evenParirtyPossible) {
            while (k > 1) {
                summands.add(2);
                n=n-2;
                k--;
            }
            if (k == 1 && n==0) {
                summands.clear();
                return summands;
            }else {
                summands.add(n);
            }
        }
        else  {
            while (k>1) {
                summands.add(1);
                n=n-1;
                k--;
            }
            summands.add(n);
        }
        return summands;
    }
}