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;
clock_t time_p = clock();
void dem() {
  time_p = clock() - time_p;
  cerr << "Time Taken : " << (float)(time_p) / CLOCKS_PER_SEC << "\n";
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  long long int n, k;
  cin >> n >> k;
  priority_queue<int> p;
  for (int i = 30; i >= 0; --i)
    if (n & (1 << i)) p.push(i);
  while (p.size() < k) {
    int t = p.top();
    p.pop();
    if (t == 0) break;
    p.push(t - 1);
    p.push(t - 1);
  }
  if (p.size() == k) {
    cout << "YES";
    cout << "\n";
    while (p.size()) {
      cout << (1 << p.top()) << " ";
      p.pop();
    }
  } else
    cout << "NO";
  return 0;
}