Problem: A positive integer x is called a power of two if it can be represented as x = 2^y, where y is a non-negative integer. So, the powers of two are 1, 2, 4, 8, 16, ....

You are given two positive integers n and k. Your task is to represent n as the sum of exactly k powers of two.

Input

The only line of the input contains two integers n and k (1 ≤ n ≤ 10^9, 1 ≤ k ≤ 2 ⋅ 10^5).

Output

If it is impossible to represent n as the sum of k powers of two, print NO.

Otherwise, print YES, and then print k positive integers b_1, b_2, ..., b_k such that each of b_i is a power of two, and ∑ _{i = 1}^{k} b_i = n. If there are multiple answers, you may print any of them.

Examples

Input


9 4


Output


YES
1 2 2 4 


Input


8 1


Output


YES
8 


Input


5 1


Output


NO


Input


3 7


Output


NO

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
int main() {
  int n, k, m;
  cin >> n >> k;
  m = k;
  int i, now;
  vector<int> ans;
  for (i = 31; i >= 0; i--) {
    while (n - (1 << i) >= k - 1 and n - (1 << i) >= 0)
      n -= (1 << i), ans.push_back(1 << i), k--;
  }
  if (n or ans.size() != m)
    cout << "NO";
  else {
    cout << "YES" << endl;
    sort(ans.begin(), ans.end());
    for (int i : ans) cout << i << ' ';
  }
}