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;
void solve() {
  long long n;
  cin >> n;
  int k;
  cin >> k;
  vector<int> v;
  if (n < k) {
    cout << "NO\n";
    return;
  }
  if (n % 2 == 1 && k % 2 == 0) {
    cout << "NO\n";
    return;
  }
  if (n % 2 == 0 && k % 2 == 0) {
    int t = 1;
    for (int i = 0; i < k; i++) {
      v.push_back(t);
    }
    t = n - k + 1;
    if (t < 1) {
      cout << "NO\n";
      return;
    }
    v[k - 1] = t;
    cout << "YES\n";
    for (int i = 0; i < k; i++) {
      cout << v[i] << " ";
    }
    cout << "\n";
    return;
  }
  if (n % 2 == 0 && k % 2 == 1) {
    int t = 2;
    for (int i = 0; i < k; i++) {
      v.push_back(t);
    }
    t = n - 2 * (k - 1);
    if (t < 2) {
      cout << "NO\n";
      return;
    }
    v[k - 1] = t;
    cout << "YES\n";
    for (int i = 0; i < k; i++) {
      cout << v[i] << " ";
    }
    cout << "\n";
    return;
  }
  if (n % 2 == 1 && k % 2 == 1) {
    int t = 1;
    for (int i = 0; i < k; i++) {
      v.push_back(t);
    }
    t = n - (k - 1);
    if (t < 1) {
      cout << "NO\n";
      return;
    }
    v[k - 1] = t;
    cout << "YES\n";
    for (int i = 0; i < k; i++) {
      cout << v[i] << " ";
    }
    cout << "\n";
    return;
  }
  return;
}
int main() {
  ios::sync_with_stdio(false), cin.tie(NULL), cout.tie(NULL);
  int tests = 1;
  cin >> tests;
  while (tests--) solve();
  return 0;
}