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:
def go():
    n, k = [int(i) for i in input().split(' ')]
    o = 'YES\n'
    if n < k:
        return 'NO'
    if k == n:
        o += ' '.join(str(1) for i in range(n))
        return o
    b = [i for i in bin(n).replace('0b', '')]
    i = len(b) - 2
    ones = 0
    if b[-1] == '1':
        ones += 1
    stack = []
    while i >= 0:
        if b[i] == '1':
            stack.append(2 ** (len(b) - i - 1))
        i -= 1
    if len(stack) + ones == k:
        o += ' '.join(str(i) for i in stack + [1] * ones)
        return o
    if len(stack) + ones > k:
        return 'NO'
    while len(stack) + ones != k and stack:
        x = stack.pop()
        if x == 2:
            ones += 2
        else:
            stack.append(x // 2)
            stack.append(x // 2)
    if len(stack) + ones == k:
        o += ' '.join(str(i) for i in stack + [1] * ones)
        return o
    return 'NO'
print(go())