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() {
  long long n, k;
  cin >> n >> k;
  long long x = __builtin_popcount(n);
  if (k > n || k < x) {
    cout << "NO" << endl;
  } else {
    cout << "YES\n";
    k = k - x;
    long long count[30] = {0};
    int i = 0;
    int a = n;
    n = 0;
    while (a > 0) {
      count[i] = a % 2;
      n++;
      a = a / 2;
      i++;
    }
    long long cur = 29;
    while (k--) {
      if (count[cur]) {
        count[cur - 1] += 2;
        count[cur]--;
      } else if (count[cur] == 0) {
        cur = cur - 1;
        k++;
      }
    }
    cur = 1;
    for (int i = 0; i < 30; i++) {
      for (int j = 0; j < count[i]; j++) {
        cout << cur << " ";
      }
      cur *= 2;
    }
    cout << endl;
  }
}