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 no():
    print('NO')
    exit(0)

n, k = map(int, input().split())
bina = list(map(int, bin(n)[2:]))
cur = bina.count(1)
if k > n or cur > k:
    no()

while cur < k:
    index = bina.index(next(x for x in bina if x > 0))
    to = index
    while to < len(bina) - 1 and pow(2, to - index + 1) - 1 <= k - cur:
        to += 1
    if to == index:
        no()
    bina[index] -= 1
    bina[to] += pow(2, to - index)
    cur += pow(2, to - index) - 1
    
print('YES')
for i in range(len(bina)):
    num = pow(2, len(bina) - i - 1)
    for j in range(bina[i]):
        print(num, end=' ')