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 N, K;
int no1, p[233333], L;
inline void add(int x) {
  if (x == 1)
    no1++;
  else
    p[++L] = x;
}
int main() {
  scanf("%d%d", &N, &K);
  for (int i = 1 << 29; i; i >>= 1)
    if (N & i) add(i);
  if (no1 + L > K || N < K) {
    puts("NO");
    return 0;
  }
  while (no1 + L < K) {
    int w = p[L--];
    add(w >> 1);
    add(w >> 1);
  }
  while (no1--) p[++L] = 1;
  puts("YES");
  for (int i = 1; i <= L; i++) printf("%d%c", p[i], " \n"[i == L]);
  return 0;
}