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;
  cin >> n >> k;
  priority_queue<int> maxh;
  int c = 0;
  if (k > n)
    cout << "NO";
  else {
    int j = 0;
    while (n >= (1 << j)) {
      if (n & (1 << j)) {
        c++;
        maxh.push(1 << j);
      }
      j++;
    }
    if (k < c)
      cout << "NO";
    else {
      cout << "YES\n";
      while (c < k) {
        int a = maxh.top();
        maxh.pop();
        maxh.push(a / 2);
        maxh.push(a / 2);
        c++;
      }
      while (maxh.size() != 0) {
        cout << maxh.top() << " ";
        maxh.pop();
      }
    }
  }
  cout << "\n";
}