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:
from heapq import heappush, heappop

class Backwards(int):
    def __lt__(self, other):
        return not int.__le__(self, other)

    def __le__(self, other):
        return not int.__lt__(self, other)

    def __gt__(self, other):
        return not int.__ge__(self, other)

    def __ge__(self, other):
        return not int.__gt__(self, other)


power = [2**i for i in range(31)]
n, k = map(int, input().split())
factors = []

while n > 0:
    for i in range(31):
        if power[i] > n:
            heappush(factors, Backwards(power[i-1]))
            n -= power[i-1]
            break

if k < len(factors):
    print('NO')
else:
    while len(factors) < k:
        if factors[0] == 1:
            break
        else:
            x = heappop(factors)
            heappush(factors, Backwards(x//2))
            heappush(factors, Backwards(x // 2))
    if len(factors) == k:
        print('YES')
        factors.sort(reverse=True)
        print(*factors)
    else:
        print('NO')