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.*;
public class Main {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int t,c,a,b,T=sc.nextInt();

        StringBuilder st=new StringBuilder();
        while (T-->0){
            a=sc.nextInt();b=sc.nextInt();
              if((a%2!=0&&b%2==0)||(b>a))st.append("NO\n");
              else{
                  if(a==b) {
                      st.append("YES\n");
                      for (t = 0; t < a; t++) st.append(1 + " ");
                      st.append("\n");
                  }else {



                          if ((a - (b - 1) * 2) % 2 == 0 && (b - 1) * 2 < a) {
                              st.append("YES\n");
                              for (t = 0; t < b - 1; t++) st.append(2 + " ");
                              st.append(a - (b - 1) * 2 + "\n");


                          } else if ((a - (b - 1)) % 2 != 0) {
                              st.append("YES\n");
                              for (t = 0; t < b - 1; t++) st.append(1 + " ");
                              st.append((a - (b - 1)) + "\n");

                          }else
                          st.append("NO\n");


                      
                  }
              }

        }
        System.out.print(st);
    }}