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 = list(bin(n)[2:])
b.reverse()
r = []
sm = 0
for i in range(len(b)):
    if b[i] == '1':
        sm += 2**int(i)
        r.append(int(i))

if len(r) > k or k > sm: print('NO')
elif len(r) == k:
    print("YES")
    for i in r: print(2**i, end = ' ')
else:
    print("YES")
    s = len(r)
    while s != k:
        if r[0] == 0:
            print(2**r[0], end = ' ')
            r.pop(0)
        else:
            r.insert(0, r[0]-1)
            r[1] = r[0]
            s += 1
    for i in r: print(2 ** i, end = ' ')