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 nos;
void split(int n) {
  if (nos == 0 || n == 1)
    cout << n << ' ';
  else {
    --nos;
    split(n / 2);
    split(n / 2);
  }
}
int main() {
  ios::sync_with_stdio(false);
  int n, k;
  cin >> k >> n;
  if (n > k)
    cout << "NO" << endl;
  else {
    vector<int> nums;
    for (int i = 0; k; k /= 2, ++i) {
      if (k % 2) nums.push_back(pow(2, i));
    }
    nos = n - nums.size();
    if (nos < 0)
      cout << "NO" << endl;
    else {
      cout << "YES" << endl;
      for (auto &i : nums) split(i);
    }
  }
  return 0;
}