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;
const int N = 31;
int ar[N + 5];
unordered_map<int, bool> mp;
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
  ;
  int n, k;
  cin >> n >> k;
  int ar[k + 5];
  int sum = k;
  bool f = true;
  for (int i = 0; i < k; i++) {
    int x = (n - sum) + 1;
    int d = log2(x * 1.0);
    int v = 1 << d;
    ar[i] = v;
    sum += (v - 1);
    if (sum > n) break;
  }
  sum = 0;
  for (int i = 0; i < k; i++) {
    sum += ar[i];
  }
  if (sum == n) {
    cout << "YES\n";
    for (int i = 0; i < k; i++) {
      cout << ar[i] << ' ';
    }
    cout << "\n";
    ;
  } else {
    cout << "NO\n";
  }
  return 0;
}