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 a[600005], n, k, mu[600], t, l;
int main() {
  cin >> n >> k;
  mu[0] = 1;
  for (int i = 1; i <= 30; i++) mu[i] = mu[i - 1] * 2;
  for (int i = 30; i >= 0; i--)
    if (n >= mu[i]) {
      n -= mu[i];
      t++;
      a[t] = mu[i];
    }
  if (t > k)
    cout << "NO";
  else {
    l = 0;
    while (t < k) {
      l++;
      while (a[l] != 1) {
        a[l] = a[l] / 2;
        t++;
        a[t] = a[l];
        if (a[l] == 0) {
          cout << "NO";
          return (0);
        }
        if (t == k) break;
      }
    }
    cout << "YES" << endl;
    for (int i = 1; i <= t; i++) cout << a[i] << ' ';
  }
}