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;
long long int poww(int a, int n) {
  long long int ans = 1;
  for (int i = 0; i < n; i++) {
    ans = ans * a;
  }
  return ans;
}
int main() {
  long long int n, k;
  cin >> n >> k;
  stack<int> q;
  long long int t = n;
  while (t != 0) {
    int rem = t % 2;
    q.push(rem);
    t = t / 2;
  }
  stack<int> s;
  while (q.empty() == false) {
    int a = q.top();
    s.push(a);
    q.pop();
  }
  int i = 0;
  int coun = 0;
  while (s.empty() == false) {
    int a = s.top();
    if (a == 1) {
      q.push(poww(2, i));
      coun++;
      s.pop();
    } else {
      s.pop();
    }
    i++;
  }
  stack<int> s1;
  stack<int> s2;
  while (q.empty() == false) {
    if (q.top() > 1) {
      s1.push(q.top());
      q.pop();
    } else {
      s2.push(q.top());
      q.pop();
    }
  }
  while (coun < k && s1.empty() == false) {
    int x = s1.top();
    s1.pop();
    x = x / 2;
    if (x > 1) {
      s1.push(x);
      s1.push(x);
      coun++;
    } else {
      s2.push(x);
      s2.push(x);
      coun++;
    }
  }
  while (s1.empty() == false) {
    s2.push(s1.top());
    s1.pop();
  }
  if (coun == k) {
    cout << "YES" << endl;
    while (s2.empty() == false) {
      int y = s2.top();
      cout << y << " ";
      s2.pop();
    }
    cout << endl;
  } else {
    cout << "NO" << endl;
  }
  return 0;
}