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())
b = format(n, 'b')
one = b.count('1')

if k<one or k>n:
    print('NO')
    exit()

print('YES')

b = list(map(int, list(b)))

for _ in range(k-one):
    for i in range(len(b)-1):
        if b[i]>=1:
            b[i] -= 1
            b[i+1] += 2
            break

b.reverse()
ans = []
t = 1

for i in range(len(b)):
    for _ in range(b[i]):
        ans.append(t)
    t *= 2

print(*ans)