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.IOException;
import java.io.InputStreamReader;
import java.math.BigDecimal;
import java.math.BigInteger;
import java.text.DecimalFormat;
import java.util.*;
import java.text.NumberFormat;
//import java.util.Arrays;
import java.util.regex.Matcher;
import java.util.regex.Pattern;
import java.util.regex.PatternSyntaxException;

public class Main {

    public static void main(String[] args) throws IOException {
        InputStreamReader r = new InputStreamReader(System.in);
        BufferedReader input = new BufferedReader(r);
        int t = Integer.parseInt(input.readLine());
        for (int s = 0; s < t; s++) {
            String temp = input.readLine();
            String[] t1 = temp.split(" ");
            long n = Long.parseLong(t1[0]);
            long k = Long.parseLong(t1[1]);
            if (k == 1) {
                System.out.println("Yes");
                System.out.println(n);
            } else {
                if (n % 2 == 1 && k % 2 == 0) {
                    System.out.println("No");
                } else {
                    if (k % 2 == n % 2) {
                        long count = n - (1 * (k - 1));
                        if (count >0) {
                            System.out.println("Yes");
                            for (int i = 0; i < k - 1; i++) {
                                System.out.print(1 + " ");
                                count = i + 1;
                            }
                            System.out.println(n - count);
                        }else{
                            System.out.println("No");
                        }
                    } else {
                        if (k > n / 2) {
                            System.out.println("No");
                        } else {
                            long count = n - (2 * (k - 1));
                            if (count > 0) {
                                System.out.println("Yes");
                                for (int i = 0; i < k - 1; i++) {
                                    System.out.print(2 + " ");

                                }
                                System.out.println(count);
                            } else {
                                System.out.println("No");
                            }
                        }
                    }

                }

            }
        }
    }
}