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 book[105];
int main() {
  int n, k, mi = 0;
  scanf("%d%d", &n, &k);
  for (int i = 0; i < 31; ++i)
    if ((1 << i) & n) ++mi, book[i] = 1;
  if (k < mi || k > n) return !printf("NO\n");
  printf("YES\n");
  for (int i = 30; ~i; --i) {
    while (book[i] && k > mi) {
      --book[i];
      book[i - 1] += 2;
      ++mi;
    }
    while (book[i] && k == mi) --book[i], printf("%d ", (1 << i));
  }
  printf("\n");
  return 0;
}