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;
signed main() {
  long long n, k;
  cin >> n >> k;
  vector<long long> ans;
  for (long long i = 30; i >= 0; --i) {
    long long t = (1 << i);
    if (n - t >= 0) {
      ans.push_back(i);
      n -= t;
    }
  }
  if (ans.size() > k) {
    cout << "NO" << endl;
    return 0;
  }
  long long null = 0;
  for (long long i = 0; i < ans.size() && ans.size() - null < k; ++i) {
    if (ans[i] == 0) continue;
    ans.push_back(ans[i] - 1);
    ans.push_back(ans[i] - 1);
    ans[i] = -1;
    null++;
  }
  if (ans.size() - null < k) {
    cout << "NO" << endl;
    return 0;
  }
  cout << "YES" << endl;
  sort(ans.begin(), ans.end());
  for (long long i = 0; i != ans.size(); ++i) {
    if (ans[i] == -1) continue;
    long long wrt = (1 << ans[i]);
    cout << wrt << endl;
  }
}