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 PYTHON):

Solution:
import heapq

def bin_powers(n):
    ans = []
    for i in range(40, -1, -1):
        if n >= (1<<i):
            heapq.heappush(ans, -(1<<i))
            n -= (1<<i)
    return ans

n, k = map(int, raw_input().split())
bin_rep = bin_powers(n)
if k > n or k < len(bin_rep):
    print 'NO'
else:
    print 'YES'
    while len(bin_rep) < k:
        curr = heapq.heappop(bin_rep)
        heapq.heappush(bin_rep, curr/2)
        heapq.heappush(bin_rep, curr/2)
    ans = sorted([-item for item in list(bin_rep)])
    print ' '.join(map(str, ans))