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 count(a):
    result = 0
    while (a != 0):
        if (a % 2 == 1):
            result += 1
        a //= 2
    return result

n, k = map(int, input().split())
if ((count(n) > k) or (k > n)):
    print("NO")
    exit(0)

components = []
a = n
while (a != 0):
    components.append(a % 2)
    a //= 2
    
#print(components)

for i in range(len(components)):
    components[i] *= 2 ** i

#print(components)

i = 0

currentResult = count(n)
while (currentResult < k):
    if (components[i] > 1):
        components[i] //= 2
        components.append(components[i])
        currentResult += 1
    else:
        i += 1

print("YES")
for i in range(len(components)):
    if (components[i] != 0):
        print(components[i], end = " ")