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;
using std::string;
priority_queue<int> q;
int main() {
  int n, k;
  cin >> n >> k;
  int num = 1;
  for (int i = 0; i < 32; i++) {
    if (((1 << i) & n) != 0) {
      q.push(num);
    }
    num *= 2;
  }
  if (k < q.size())
    cout << "NO";
  else {
    while (q.size() < k) {
      int num = q.top();
      q.pop();
      if (num == 1) break;
      num /= 2;
      q.push(num);
      q.push(num);
    }
    if (q.size() == k) {
      cout << "YES" << endl;
      while (!q.empty()) {
        cout << q.top() << " ";
        q.pop();
      }
    } else
      cout << "NO";
  }
}