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;
queue<long long> q;
long long ans, n, i, j, k, l, m, x = 0;
int main() {
  cin >> n >> k;
  if (n < k || (k < __builtin_popcount(n)))
    return cout << "NO", 0;
  else
    cout << "YES\n";
  while (n > 0) {
    ans = n & 1;
    if (ans == 1) q.push((1ll << x));
    x++;
    n = (n >> 1);
  }
  while (q.size() != k) {
    x = q.front();
    q.pop();
    if (x != 1)
      q.push(x / 2), q.push(x / 2);
    else
      q.push(x);
  }
  while (!q.empty()) cout << q.front() << "  ", q.pop();
}