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;
int32_t main() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  long long q;
  cin >> q;
  while (q--) {
    long long n, k;
    cin >> n >> k;
    vector<long long> e, o;
    long long esum = n, osum = n;
    for (long long i = 0; i + 1 < k; i++) {
      e.push_back(2);
      o.push_back(1);
      osum -= 1;
      esum -= 2;
    }
    if (esum > 0 && esum % 2 == 0) {
      e.push_back(esum);
      cout << "YES" << '\n';
      for (auto x : e) {
        cout << x << " ";
      }
      cout << '\n';
    } else if (osum > 0 && osum % 2 == 1) {
      o.push_back(osum);
      cout << "YES" << '\n';
      for (auto x : o) {
        cout << x << " ";
      }
      cout << '\n';
    } else
      cout << "NO" << '\n';
  }
}