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() {
  long long int n, k, i, count = 0, temp;
  vector<long long int> v;
  cin >> n >> k;
  for (i = n; i >= 1; i = i / 2) {
    v.push_back(i % 2);
    if (i % 2 == 1) {
      count++;
    }
  }
  if (k < count || k > n) {
    cout << "NO";
    return 0;
  }
  for (i = v.size() - 1; i >= 0; i--) {
    if (count != k) {
      temp = min(v[i], k - count);
      count += temp;
      v[i] -= temp;
      v[i - 1] += 2 * temp;
    }
  }
  cout << "YES" << endl;
  for (i = 0; i < v.size(); i++) {
    if (v[i] != 0) {
      for (auto j = 0; j < v[i]; j++) {
        cout << (long long int)pow(2, i) << " ";
      }
    }
  }
}