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 t[31];
int main() {
  int a, k;
  cin >> a >> k;
  if (k > a) {
    cout << "NO";
    return 0;
  }
  int x = 0;
  int i = 0;
  while (a > 0) {
    if (a % 2 == 1) {
      x++;
      t[i]++;
    }
    i++;
    a = a / 2;
  }
  i = 30;
  if (x > k) {
    cout << "NO";
    return 0;
  }
  cout << "YES\n";
  while (t[i] == 0) {
    i--;
  }
  while (x < k) {
    while (t[i] == 0) {
      i--;
    }
    t[i]--;
    t[i - 1] += 2;
    x++;
  }
  for (i = 0; i <= 30; i++) {
    for (int j = 0; j < t[i]; j++) {
      cout << (1 << i) << " ";
    }
  }
  return 0;
}