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:
n, k = list(map(int, input().split()))

bin_array = list(map(int, bin(n)[:1:-1]))
while len(bin_array) > 1 and sum(bin_array) < k:
    bin_array[-2] += 2
    bin_array[-1] -= 1
    if bin_array[-1] == 0:
        bin_array.pop()

if sum(bin_array) != k:
    print('NO')
    exit()

print('YES')
print(' '.join(str(2**i)
               for i, x in enumerate(bin_array)
               for j in range(x)))