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() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
  long long n, k, hold = 1;
  priority_queue<long long> pq;
  cin >> n >> k;
  if (k > n) {
    cout << "NO";
    return 0;
  }
  while (hold <= n) {
    if (n & hold) {
      pq.push(hold);
    }
    hold = hold << 1;
  }
  long long a = pq.size();
  if (a > k) {
    cout << "NO";
    return 0;
  }
  long long b = k - a;
  for (int i = 0; i < b; i++) {
    long long cur = pq.top();
    pq.pop();
    if (cur == 1)
      break;
    else {
      pq.push(cur / 2);
      pq.push(cur / 2);
    }
  }
  cout << "YES" << endl;
  for (int i = 0; i < k; i++) {
    cout << pq.top() << " ";
    pq.pop();
  }
  return 0;
}