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>
int a[100];
int min(int a, int b) { return a < b ? a : b; }
int main() {
  int n, k, sum = 0;
  scanf("%d%d", &n, &k);
  for (long long i = 1, t = 0; i <= n; i <<= 1, t++)
    if (n & i) {
      a[t]++;
      sum++;
    }
  if (sum > k || k > n)
    puts("NO");
  else {
    puts("YES");
    int p = k - sum;
    for (int i = 32; i; i--) {
      int t = min(a[i], p);
      a[i] -= t;
      a[i - 1] += t + t;
      p -= t;
    }
    for (int i = 1, t = 0; t <= 32; i <<= 1, t++)
      for (int k = 1; k <= a[t]; k++) printf("%d ", i);
  }
  return 0;
}