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 n, k;
int main() {
  cin >> n >> k;
  int x = 1;
  priority_queue<int> que;
  for (int i = 0; i < 32; ++i) {
    if (x & n) que.push(x);
    x <<= 1;
  }
  while (que.size() < k && que.top() > 1) {
    x = que.top();
    que.push(x / 2);
    que.push(x / 2);
    que.pop();
  }
  if (que.size() > k || que.size() < k) {
    cout << "NO";
    return 0;
  }
  cout << "YES\n";
  while (!que.empty()) {
    cout << que.top() << ' ';
    que.pop();
  }
}