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;
int32_t main() {
  long long n, k, i;
  cin >> n >> k;
  long long b = __builtin_popcount(n);
  if (k > n || k < b) {
    cout << "NO\n";
    return 0;
  }
  cout << "YES\n";
  priority_queue<long long> q;
  for (i = 0; i <= 30; i++) {
    if (n & (1LL << i)) {
      q.push(1LL << i);
    }
  }
  while (q.size() < k) {
    long long t = q.top();
    q.pop();
    q.push(t >> 1);
    q.push(t >> 1);
  }
  while (q.size()) {
    cout << q.top() << " ";
    q.pop();
  }
}