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.text.NumberFormat;
import java.util.Arrays;
import java.util.Locale;
import java.util.Scanner;

public class Main {
    //new declaration
    //shortcut declaration
    //concatenation
    //length
    //toLowerCase(), toUpperCase()
    //startsWith(), endsWith()
    //indexOf()
    //trim()
    //replace()
    //immutablity()
    //Hello \"arfin"
    //c:\\Windows\...
    //\n \t

    //Arrays
    //Variable to array
    //Exception Peak
    //Printing array Address
    //Arrays Class to print
    //Curly Braces declaration
    //Array Lenght
    //Array Sort
    //deepToString()
    //int[][] ara = {{1,2,3}, {4,5,6}};
    //System.out.println(Arrays.deepToString(ara));
    public static void main(String[] args) {
//        int[][] ara = {{1,2,3}, {4,5,6}};
//        System.out.println(Arrays.deepToString(ara));
//        final int PI = 3;
//        double val = 5.0 / 2;
//        System.out.println(val);
//        int x = 1;
//        x++;
//        ++x;
//        int y = ++x;
//        System.out.println(y);
//        System.out.println(x);

//        int m = (10 + 3) * 3; // (), */, +-
//        System.out.println(m);

        //*Casting
        //Implicit Casting - Automatic Conversion
        //byte > short > int > long > float > double
        //Explicit Casting (int)
        //Only compatble types
//        String x = "2"; // 2 byte
//        double z = Double.parseDouble(x) + 4; // 4 byte
//        System.out.println(z);
//
//        //==The math class
//        Math.max(1, 2);
//        Math.min(1, 2);
//        Math.round(2.3F);
//        Math.ceil(2.3F);
//        Math.random();
//        long randNum = Math.round(Math.random() * 100);
//
//        //==Formating Numbers
//        //$123,456,789
//        //0.1% -> 10%
//        System.out.println(NumberFormat.getInstance());

        Scanner scanner = new Scanner(System.in);
        int testCase = scanner.nextInt();
        for(int testRunning = 1; testRunning <= testCase; testRunning++){
            int n = scanner.nextInt();
            int k = scanner.nextInt();

            int kOdd = (k-1)*1;

            int remainingOdd = n - kOdd;
            if(kOdd < n && remainingOdd %2 == 1){
                System.out.println("YES");
                for(int i = 0; i < k-1; i++){
                    System.out.print(1 + " ");
                }
                System.out.println(remainingOdd);
                continue;
            }

            int kEven = (k-1)*2;
            int remainingEven = n - kEven;
            if(kEven < n && (remainingEven)%2 == 0){
                System.out.println("YES");
                for(int i = 0; i < k-1; i++){
                    System.out.print(2 + " ");
                }
                System.out.println(remainingEven);
                continue;
            }

            System.out.println("NO");


        }

    }
}