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;
  vector<int> v;
  int count = 0, ck = 0;
  cin >> n >> k;
  if (k < __builtin_popcount(n) || k > n) {
    cout << "NO" << endl;
    return 0;
  }
  while (n) {
    if (n & 1) {
      v.push_back(1 << count);
    }
    n = n >> 1;
    count++;
  }
  while (1) {
    for (int i = 0; i < v.size(); i++) {
      if (v.size() >= k) {
        ck = 1;
        break;
      }
      if (v[i] > 1) {
        v[i] = v[i] / 2;
        v.push_back(v[i]);
      }
    }
    if (ck) break;
  }
  if (v.size() > k)
    cout << "NO" << endl;
  else if (v.size() == k) {
    cout << "YES" << endl;
    for (auto it : v) cout << it << " ";
  }
  return 0;
}