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;
bool sortinrev(const pair<long long int, long long int> &a,
               const pair<long long int, long long int> &b) {
  return (a.first > b.first);
}
bool sortbysec(const pair<long long int, long long int> &a,
               const pair<long long int, long long int> &b) {
  return (a.second < b.second);
}
int dx[4] = {0, -1, 0, 1};
int dy[4] = {1, 0, -1, 0};
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  long long int t;
  cin >> t;
  while (t--) {
    long long int n, k;
    cin >> n >> k;
    long long int rem = n - k;
    vector<long long int> v;
    bool f = 0;
    if (n < k) f = 1;
    if (rem % 2 == 0) {
      v.assign(k, 1);
      v[0] += rem;
    } else {
      rem -= k;
      v.assign(k, 2);
      if (rem >= 0 && rem % 2 == 0)
        v[0] += rem;
      else
        f = 1;
    }
    if (f)
      cout << "NO" << endl;
    else {
      cout << "YES" << endl;
      for (auto x : v) cout << x << " ";
      cout << endl;
    }
  }
  return 0;
}