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:
n, k = map(int, input().split())
a = bin(n)[:1:-1]
d = dict()
m = 0
for i, x in enumerate(a):
    d[1 << i] = x == '1'
    m += d[1 << i]
if k > n or k < m:
    print('NO')
    exit()
print('YES')
while m < k:
    p = k - m
    g = min(d[1 << i], p)
    d[1 << i] -= g
    i -= 1
    d[1 << i] += 2 * g
    m += g
r = []
for x in d:
    r += [x] * d[x]
print(*r)