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:
# Created by nikita at 30/12/2018

n, k = [int(i) for i in input().split()]

s = bin(n)

stack = []

j = 0
for i in reversed(s):
    if i == '1':
        stack.append(2 ** j)
    j += 1

if len(stack) > k or n < k:
    print("NO")
    exit(0)

ones = 0

while len(stack) != k - ones:
    while True:
        tmp = stack.pop()
        if tmp != 1:
            break
        else:
            ones += 1
    stack.append(tmp // 2)
    stack.append(tmp // 2)

print("YES")
print(*[1 for i in range(ones)], end = ' ')
print(*stack)