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 a, k;
  cin >> a >> k;
  vector<int> b, binary;
  int counter = 0;
  while (a > 0) {
    if (a % 2 == 1) {
      b.push_back(1 << counter);
    }
    a = a / 2;
    counter++;
  }
  if (b.size() > k) {
    cout << "NO";
  } else {
    int left = 0;
    while (b.size() != k && left < b.size()) {
      if (b[left] % 2 == 0 && b[left] != 0) {
        b.push_back(b[left] / 2);
        b[left] = b[left] / 2;
      } else
        left++;
    }
    if (b.size() != k) {
      cout << "NO";
      return 0;
    }
    cout << "YES" << endl;
    for (int i = 0; i < b.size(); i++) {
      cout << b[i] << " ";
    }
  }
}