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 n, k, cnt[40], Pow[40], dem, dem1;
int main() {
  cin >> n >> k;
  if (k > n) {
    cout << "NO";
    return 0;
  }
  while (n > 0) {
    if (n % 2 == 1) {
      cnt[dem1]++;
      dem++;
    }
    dem1++;
    n /= 2;
  }
  if (dem > k) {
    cout << "NO";
    return 0;
  }
  for (int i = 30; i >= 0; i--)
    if (cnt[i] > 0) {
      while (dem < k && cnt[i] > 0) {
        cnt[i - 1] += 2;
        cnt[i]--;
        dem++;
      }
    }
  cout << "YES" << endl;
  Pow[0] = 1;
  for (int i = 1; i <= 30; i++) Pow[i] = Pow[i - 1] * 2;
  for (int i = 0; i <= 30; i++)
    for (int j = 1; j <= cnt[i]; j++) cout << Pow[i] << " ";
  return 0;
}