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 n, k;
vector<int> ans;
int main() {
  cin >> n >> k;
  if (k > n) {
    cout << "NO";
    return 0;
  }
  for (int i = 30; i >= 0; i--) {
    while (n >= (1 << i)) {
      n -= (1 << i);
      ans.push_back(1 << i);
    }
  }
  if ((int)ans.size() > k)
    cout << "NO";
  else {
    int t = 0;
    while (k > ans.size()) {
      while (ans[t] <= 1) t++;
      ans[t] /= 2;
      ans.push_back(ans[t]);
    }
    cout << "YES" << endl;
    for (int i = 0; i < ans.size(); i++) cout << ans[i] << " ";
  }
  return 0;
}