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:
import heapq

n,k = map(int, input().split())
s = bin(n)[2:]
minval = s.count("1")
maxval = n

if k >= minval and k <= maxval:
    print("YES")
    L = []
    for i,x in enumerate(s[::-1]):
        if x == "1":
            heapq.heappush(L,-2**i)
        
    while len(L) != k:
        current = heapq.heappop(L)
        heapq.heappush(L, current // 2)
        heapq.heappush(L, current // 2)
        
    print(" ".join([str(-x) for x in L]))
else:
    print("NO")