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 CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
int main() {
  int t, i, j;
  cin >> t;
  int a[t][2];
  for (i = 0; i < t; i++) cin >> a[i][0] >> a[i][1];
  for (i = 0; i < t; i++) {
    if (a[i][0] >= a[i][1]) {
      if (a[i][0] % 2) {
        if (a[i][1] % 2) {
          cout << "YES\n";
          for (j = 0; j < a[i][1] - 1; j++) cout << 1 << " ";
          cout << a[i][0] - a[i][1] + 1 << "\n";
        } else
          cout << "NO\n";
      } else {
        if (!(a[i][1] % 2)) {
          cout << "YES\n";
          for (j = 0; j < a[i][1] - 1; j++) cout << 1 << " ";
          cout << a[i][0] - a[i][1] + 1 << "\n";
        } else if (a[i][1] <= a[i][0] / 2) {
          cout << "YES\n";
          for (j = 0; j < a[i][1] - 1; j++) cout << 2 << " ";
          cout << a[i][0] - 2 * a[i][1] + 2 << "\n";
        } else
          cout << "NO\n";
      }
    } else
      cout << "NO\n";
  }
  return 0;
}