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:
# C - Powers Of Two 

n, k = map(int, input().split())
binN = list(map(int, bin(n)[2:]))

c = binN.count(1)
if k < c or k > n:
    print('NO')
else:
    i = 0
    while i < len(binN) - 1 and c < k:
        while binN[i] > 0 and c < k:
            c = c + 1
            binN[i] = binN[i] - 1
            binN[i + 1] = binN[i + 1] + 2
        i = i + 1

    i = len(binN) - 1
    output = []
    while i >= 0:
        while(binN[i] > 0):
            output.append(2 ** (len(binN) - i - 1))
            binN[i] = binN[i] - 1
        i = i - 1
    print('YES')
    print(' '.join(map(str, output)))