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;
bool gb(long long a, long long b) { return (a >> b) & 1; }
signed main() {
  long long n, k, t = 0;
  cin >> n >> k;
  vector<long long> ans(32, 0);
  for (long long i = 0; i < 31; i++) {
    if (gb(n, i)) {
      ans[i]++;
      t++;
    }
  }
  long long res = k - t;
  if (k < t || k > n) {
    cout << "NO";
    exit(0);
  } else {
    for (long long i = 31; i > 0; --i) {
      if (res > ans[i]) {
        ans[i - 1] += 2 * ans[i];
        res -= ans[i];
        ans[i] = 0;
      } else {
        ans[i - 1] += 2 * res;
        ans[i] -= res;
        break;
      }
    }
  }
  cout << "YES" << endl;
  for (long long i = 0; i < 32; ++i) {
    for (long long j = 0; j < ans[i]; ++j) {
      cout << (1 << i) << " ";
    }
  }
}