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 arr[31];
map<int, int> mp;
void Set() {
  for (int i = 0; i < 31; i++) {
    arr[i] = (1 << i);
  }
}
int main() {
  Set();
  int n, k, cnt = 0;
  cin >> n >> k;
  bool ok = false;
  for (int i = 30; i >= 0; i--) {
    if (n == 0) {
      break;
    }
    if (arr[i] <= n) {
      n -= arr[i];
      mp[arr[i]]++;
      i++;
      cnt++;
    }
  }
  cerr << "cnt"
       << " " << cnt << '\n';
  if (cnt > k) {
    cout << "NO\n";
    return 0;
  } else if (cnt == k) {
    cout << "YES\n";
    for (int i = 0; i < 31; i++) {
      if (mp[arr[i]]) {
        for (int j = 0; j < mp[arr[i]]; j++) {
          cout << arr[i] << " ";
        }
      }
    }
    cout << '\n';
    return 0;
  }
  int nd = k - cnt;
  cerr << "nd"
       << " " << nd << '\n';
  while (1) {
    bool found = false;
    for (int i = 0; i < 31; i++) {
      if (mp[arr[i]] and arr[i] > 1) {
        mp[arr[i]]--;
        mp[arr[i] / 2] += 2;
        found = true;
        cnt++;
        break;
      }
    }
    if (cnt == k or !found) break;
  }
  if (cnt == k) {
    cout << "YES\n";
    for (int i = 0; i < 31; i++) {
      if (mp[arr[i]]) {
        for (int j = 0; j < mp[arr[i]]; j++) {
          cout << arr[i] << " ";
        }
      }
    }
    cout << '\n';
  } else
    cout << "NO\n";
  return 0;
}