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.*;
import java.util.*;

/**
 * Created by Ayushi on 09 May 2020.
 * Problem:
 * Round:
 */

public class B {
    public static void main(String[] args) throws IOException {
        StringTokenizer st;
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        int t = Integer.parseInt(br.readLine());

        while (t-- > 0) {
            st = new StringTokenizer(br.readLine(), " ");
            int n = Integer.parseInt(st.nextToken());
            int k = Integer.parseInt(st.nextToken());

            if (k > n) {
                System.out.println("NO");
            }
            else if (n == k) {
                System.out.println("YES");
                for (int i = 0; i < k; i++) System.out.print("1 ");
                System.out.println();
            }
            else {
                if (n % 2 == 0) {
                    if (k > n/2) {
                        if (k % 2 == 1) {
                            System.out.println("NO");
                        }
                        else {
                            System.out.println("YES");
                            for (int i = 0; i < k-1; i++) System.out.print("1 ");
                            System.out.println(n-(k-1));
                        }
                    }
                    else {
                        System.out.println("YES");
                        for (int i = 0; i < k-1; i++) System.out.print("2 ");
                        System.out.println(n-(2*(k-1)));
                    }
                }
                else {
                    if (k % 2 == 0) System.out.println("NO");
                    else {
                        System.out.println("YES");
                        for (int i = 0; i < k-1; i++) System.out.print("1 ");
                        System.out.println(n-(k-1));
                    }
                }
            }
            /*else if ((n % 2 == 0 && (k > (n / 2)))) {
                System.out.println("NO");
            }*/
            /*else if (n % 2 == 1 && k % 2 == 0){
                System.out.println("NO");
            }*/
            /*else {
                System.out.println("YES");
                for (int i = 0; i < k-1; i++) {
                    System.out.print(((n % 2) == 0) ? "2 " : "1 ");
                }
                System.out.println(n-((k-1)*(((n % 2) == 0) ? 2:1)));
            }*/
        }
        br.close();
    }
}