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 main() {
  ios::sync_with_stdio(0), cin.tie(NULL), cout.tie(NULL);
  cin >> n >> k;
  queue<int> pw;
  for (int i = 0; i < 31; i++) {
    if (n & 1 << i) {
      pw.push(1 << i);
    }
  }
  int h = k;
  if (k > n) {
    cout << "NO\n";
  } else {
    k -= pw.size();
    if (k < 0) {
      cout << "NO\n";
      return 0;
    }
    cout << "YES\n";
    for (int i = 0; i < h;) {
      if (pw.front() == 1 || k == 0) {
        cout << pw.front() << " ";
        pw.pop();
        i++;
      } else {
        int x = pw.front();
        pw.pop();
        pw.push(x / 2);
        pw.push(x / 2);
        k--;
      }
    }
  }
  return 0;
}