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;
multiset<int> s;
int main() {
  int n, k;
  scanf("%d%d", &n, &k);
  for (int i = 30; i >= 0; i--) {
    if (n & (1 << i)) s.insert(i);
  }
  int len = s.size();
  if (n < k || len > k) {
    printf("NO");
  } else {
    printf("YES\n");
    multiset<int>::iterator i;
    while (s.size() < k) {
      i = (--s.end());
      int now = *i;
      s.erase(i);
      s.insert(now - 1);
      s.insert(now - 1);
    }
    for (i = s.begin(); i != s.end(); i++) {
      printf("%d ", 1 << *i);
    }
  }
  return 0;
}