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;
priority_queue<long long, vector<long long>, less<long long> > Q;
int main() {
  long long N, i, j, k, K;
  cin >> N >> K;
  vector<int> X;
  k = 0;
  for (i = 32; i >= 0; i--) {
    if ((1LL << i) & N) {
      Q.push(1LL << i);
      k++;
    }
  }
  int ptr = 0;
  while (k < K && ptr < 1000000) {
    int x = Q.top();
    Q.pop();
    if (x % 2 == 0) {
      Q.push(x / 2);
      Q.push(x / 2);
      k++;
    }
    ptr++;
  }
  if (k != K) {
    cout << "NO\n";
    return 0;
  }
  cout << "YES\n";
  while (!Q.empty()) {
    cout << Q.top() << " ";
    Q.pop();
  }
  return 0;
}