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 PYTHON3):

Solution:
def GETBIT(x, bit):
    return (x >> bit) & 1

def solve(n, k):
    if (n < k):
        print("NO")
        return
    sbit = 0
    lst = [0] * k
    for i in range(30):
      if GETBIT(n, i) == 1:
          sbit += 1
          if sbit <= k:
              lst[sbit-1] = i
    if sbit > k:
        print("NO")
        return
    cnt = sbit
    pos = sbit - 1
    while cnt < k and pos >= 0:
        if lst[pos] == 0:
            pos -= 1
            continue
        lst[pos] = lst[pos] - 1
        #print(cnt, pos, lst[pos])
        lst[pos+1] = lst[pos]
        pos += 1
        cnt += 1
    if cnt < k:
        print("NO")
        return
    print("YES")
    print(*((1 << lst[i]) for i in range(k)))

n, k = map(int, input().split())
solve(n, k)