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() {
  long long k, n;
  long long min_tot = 0;
  cin >> k >> n;
  long long num = k;
  multiset<long long> ms;
  int i = 0;
  while (k > 0) {
    if (k % 2 == 1) {
      ms.insert(pow(2, i * (k % 2)));
    }
    i++;
    min_tot += k % 2;
    k = k / 2;
  }
  long long t;
  if (min_tot <= n && n <= num) {
    while (ms.size() != n) {
      t = *(ms.rbegin());
      ms.insert(t / 2);
      ms.insert(t / 2);
      ms.erase(--ms.end());
    }
    cout << "YES" << endl;
    for (int x = 0; x < n; x++) {
      cout << *(ms.rbegin()) << " ";
      ms.erase(--ms.end());
    }
    cout << endl;
  } else {
    cout << "NO" << endl;
  }
}