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() {
  cin.sync_with_stdio(false);
  cin.tie(0);
  int n, k;
  cin >> n >> k;
  int bits = __builtin_popcount(n);
  if (n < k || bits > k) return 0 * puts("NO");
  vector<int> resp;
  for (int i = 0; i < 31; ++i)
    if ((n & (1 << i))) resp.push_back(1 << i);
  int idx = resp.size() - 1;
  while (resp.size() < k) {
    int j = resp[idx];
    if (j >= 2) {
      resp.erase(resp.begin() + idx);
      resp.push_back(j / 2);
      resp.push_back(j / 2);
      idx = resp.size() - 1;
    }
    --idx;
  }
  cout << "YES\n";
  for (int i : resp) cout << i << " ";
  cout << endl;
  return 0;
}