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, i, x = 1;
  cin >> n >> k;
  long long a[40];
  if (k <= n) {
    for (i = 0; n > 0; n /= 2, i++) k -= (a[i] = n % 2);
    n = i;
    if (k < 0) {
      cout << "NO";
      return 0;
    } else
      cout << "YES" << endl;
    for (--i; k > 0; i--)
      while (a[i] && k > 0) a[i]--, a[i - 1] += 2, k--;
    for (i = 0; i < n; i++) {
      for (int j = 0; j < a[i]; j++) cout << x << " ";
      x *= 2;
    }
  } else
    cout << "NO";
}