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 power[32];
bool flag = 0;
bool dfs(int n, int k) {
  if (n < k || __builtin_popcount(n) > k) return 0;
  if (n < 0 || k < 0) return 0;
  if (n == 0 && k == 0) {
    cout << "YES\n";
    return 1;
  }
  int cnt = 0;
  while ((1 << cnt) < n) cnt++;
  for (int i = cnt; i >= 0; i--) {
    if (dfs(n - (1 << i), k - 1)) {
      cout << (1 << i) << ' ';
      return 1;
    }
  }
  return 0;
}
int main() {
  int n, k;
  cin >> n >> k;
  for (int i = 0; i <= 30; i++) power[i] = 1 << i;
  if (!dfs(n, k)) cout << "NO";
}