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() {
  long long n, k;
  cin >> n >> k;
  vector<long long> vc;
  long long i = 0;
  while (n > 0) {
    if (n % 2) vc.push_back(pow(2, i));
    n /= 2;
    i++;
  }
  for (long long i = 0; i < vc.size() and vc.size() < k; i++) {
    while (vc[i] > 1 and vc.size() < k) {
      vc.push_back(vc[i] / 2);
      vc[i] = vc[i] / 2;
    }
  }
  if (vc.size() == k) {
    cout << "YES" << endl;
    for (long long i = 0; i < vc.size(); i++) cout << vc[i] << ' ';
  } else
    cout << "NO" << endl;
}