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() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
  long long int n, k;
  cin >> n >> k;
  long long int sb = __builtin_popcount(n);
  if (k > n || k < sb) {
    cout << "NO\n";
  } else {
    multiset<long long int> mm;
    for (long long int i = 0; i < 32; i++) {
      if ((n >> i) & 1) {
        mm.insert((1 << i));
      }
    }
    while ((long long int)mm.size() < k) {
      auto it = *(mm.rbegin());
      mm.erase(mm.find(it));
      mm.insert((it) / 2);
      mm.insert((it) / 2);
    }
    cout << "YES\n";
    for (auto i : mm) {
      cout << i << " ";
    }
  }
}