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, x = map(int, input().split())
v = n
l = []
i = 0
for k in range(32):
    if (n & (1 << k)) >> k:
        l.append(pow(2, k))

x -= len(l)
if x < 0:
    print("NO")
else:
    i = 0
    while x > 0:
        while i < len(l) and l[i] == 1:
            i += 1
        if i == len(l):
            print("NO")
            exit()
        l[i] //= 2
        l.insert(i, l[i])
        x -= 1
    l = list(map(str, l))
    print("YES")
    print(" ".join(l))