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 p[31];
int main() {
  cin >> n >> k;
  int kk = k;
  vector<int> res;
  p[0] = 1;
  for (int i = 1; i <= 30; i++) {
    p[i] = p[i - 1] * 2;
  }
  while (1) {
    if (k == 0) {
      break;
    }
    int pos = -1;
    for (int i = 0; i <= 30; i++) {
      if (k - 1 <= n - p[i]) {
        pos = i;
      }
    }
    if (pos == -1) {
      cout << "NO";
      return 0;
    }
    n -= p[pos];
    res.push_back(p[pos]);
    k--;
  }
  if (n > 0) {
    cout << "NO";
    return 0;
  }
  cout << "YES" << endl;
  for (int i = 0; i < kk; i++) {
    cout << res[i] << ' ';
  }
  return 0;
}