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;
priority_queue<int> pq;
int n, k;
bool solve() {
  int x = 1;
  while (n) {
    if (n & 1) pq.push(x);
    x <<= 1;
    n >>= 1;
  }
  if (pq.size() > k) return 0;
  while (pq.top() != 1 and pq.size() < k) {
    int t = pq.top() >> 1;
    pq.pop();
    pq.push(t);
    pq.push(t);
  }
  return (pq.size() == k ? 1 : 0);
}
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  cin >> n >> k;
  if (!solve()) return cout << "NO", 0;
  cout << "YES\n";
  while (pq.size()) {
    cout << pq.top() << ' ';
    pq.pop();
  }
  return 0;
}