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, m, k;
  map<int, int> mp;
  queue<int> q;
  cin >> n >> k;
  for (int i = 0; i <= 30; i++) {
    if (n & (1 << i)) {
      if (i > 0) q.push(1 << i);
      mp[1 << i]++;
    }
  }
  if (int(mp.size()) > k) {
    cout << "NO";
    return 0;
  }
  int len = mp.size();
  while (len < k && !q.empty()) {
    int num = q.front();
    q.pop();
    mp[num]--;
    mp[num / 2] += 2;
    if (num / 2 > 1) {
      q.push(num / 2);
      q.push(num / 2);
    }
    len++;
  }
  if (len < k) {
    cout << "NO";
    return 0;
  }
  cout << "YES\n";
  for (map<int, int>::iterator it = mp.begin(); it != mp.end(); it++) {
    for (int j = 0; j < it->second; j++) cout << it->first << ' ';
  }
  return 0;
}