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.math.BigInteger;
        import java.util.Arrays;
        import java.util.Scanner;
public class Main {
    public static StreamTokenizer in;
    static {
        try{
            in = new StreamTokenizer(new BufferedReader(new InputStreamReader(new BufferedInputStream(System.in))));
        }catch (Exception e){
            e.printStackTrace();
        }
    }
    public static int nextInt() throws IOException{ in.nextToken(); return (int)in.nval; }
    public static void main(String[] args) throws IOException{
        Scanner sc=new Scanner(new BufferedInputStream(System.in));
        int t=nextInt();
        while(t-->0){
            int n=nextInt();
            int k=nextInt();
            if(n<k)
                System.out.println("NO");
            else{
                if(n%2==1&&k%2==0)
                    System.out.println("NO");
                else if(n%2==0&&k%2==1){
                    if(n<2*k)
                        System.out.println("NO");
                    else{
                        System.out.println("YES");
                        while(k-->1){
                            System.out.print("2 ");
                            n-=2;
                        }
                        System.out.println(n);
                    }
                }else {
                    System.out.println("YES");
                    while (k-->1) {
                        System.out.print("1 ");
                        n--;
                    }
                    System.out.println(n);
                }
            }
        }
    }
}