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:
pt = []

for i in range(31):
    pt.append(2**i)
pt = pt[::-1]

n, k = map(int, input().split())

def divide(a, g):
    i = 0
    while len(a) != g:
        if a[i] == 1:
            i += 1
        else:
            e = a.pop(i)
            a.append(e//2)
            a.append(e//2)
            
    return a

if k > n:
    print("NO")
else:
    ps = []
    for i in pt:
        if i <= n:
            n = n- i
            ps.append(i)
            
    if len(ps) > k:
        print("NO")
    elif len(ps) < k:
        print("YES")
        print(" ".join(map(str, divide(ps, k))))
    else:
        print("YES")
        print(" ".join(map(str, ps)))