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:
from heapq import heappush
from heapq import heappop

a = []
x = 0
i = 0
while x < 1000000000:
    x = pow(2, i)
    a.append(x)
    i += 1

n, k = map(int, raw_input().split())

x = n
h = []
i = len(a) - 1
while x > 0:
    if x >= a[i]:
        x -= a[i]
        heappush(h, -a[i])
    else: i -= 1

if k > n or len(h) > k:
    print 'NO'
else:
    while len(h) < k:
        x = -heappop(h)
        if x == 1: break
        heappush(h, -x / 2)
        heappush(h, -x / 2)

    if len(h) == k:
        print 'YES'
        print ' '.join(map(lambda x: str(-x), h))
    else:
        print 'NO'