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.*;
import java.io.*;
public class Main {
  public static void main(String[] args) throws IOException{
      BufferedReader b1 = new BufferedReader(new InputStreamReader(System.in));
      int t = Integer.parseInt(b1.readLine());
      while(t-->0) {
          String [] vals = (b1.readLine()).split(" ");
          long n = Integer.parseInt(vals[0]);
          long k = Integer.parseInt(vals[1]);
          if(k > n) {
              System.out.println("NO");
          }
          else if(n % k == 0) {
              System.out.println("YES");
              for(int i = 0; i<k; i++) {
                  System.out.print((n/k) + " ");
              }
              System.out.println();
          }
          else {
              if(n % 2 == 0 && k % 2 == 1) {
                  if(2 * k > n) {
                      System.out.println("NO");
                  }
                  else {
                      System.out.println("YES");
                      int sum = 0;
                      for(int i = 0; i<k-1; i++) {
                          System.out.print(2 + " ");
                          sum += 2;
                      }
                      System.out.print(n - sum);
                      System.out.println();
                  }
              }
              else {
                  if(n % 2 == 1 && k % 2 == 1 || (n % 2 == 0 && k % 2 == 0)) {
                      System.out.println("YES");
                      int sum = 0;
                      for(int i = 0; i<k-1; i++) {
                          System.out.print(1 + " ");
                          sum++;
                      }
                      System.out.print(n - sum);
                      System.out.println();
                  }
                  else {
                      System.out.println("NO");
                  }
              }
          }
      }
  }
}