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() {
  int n, k;
  cin >> n >> k;
  int y = n;
  if (k > n)
    cout << "NO";
  else {
    long long x = 1, y = n;
    stack<int> st;
    while (y > 0) {
      if (y % 2) st.push(x);
      x = x << 1;
      y = y >> 1;
    }
    if (k < st.size())
      cout << "NO";
    else {
      cout << "YES"
           << "\n";
      int z = st.size();
      while (z < k) {
        if (st.top() == 1) {
          cout << st.top() << " ";
          st.pop();
        } else {
          int z1 = st.top();
          st.pop();
          st.push(z1 / 2);
          st.push(z1 / 2);
          z++;
        }
      }
      while (!st.empty()) cout << st.top() << " ", st.pop();
    }
  }
  return 0;
}