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;
  int m, i, a;
  multiset<int> s;
  cin >> n >> k;
  m = n;
  i = 0;
  while (m) {
    if (m & 1) {
      s.insert(1 << i);
    }
    i++;
    m = m >> 1;
  }
  if ((n < k) || (s.size() > k)) {
    cout << "NO" << endl;
  } else {
    while (s.size() < k) {
      a = *(--s.end());
      s.erase(--s.end());
      if (a == 1) {
        break;
      }
      s.insert(a / 2);
      s.insert(a / 2);
    }
    cout << "YES" << endl;
    while (s.size()) {
      cout << *(s.begin()) << " ";
      s.erase(s.begin());
    }
  }
}