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())
s = []
while n : 
    s.append(n & -n)
    n &= n - 1

ones = list(filter(lambda x : x == 1, s))
rem = list(filter(lambda x : x > 1, s))

def split() :
    if len(rem) == 0:
        print('NO')
        exit(0)
    x = rem.pop()
    if x == 2 :
        ones.append(1)
        ones.append(1)
    else :
        rem.append(x >> 1)
        rem.append(x >> 1)

k -= len(ones) + len(rem)

if k < 0 :
    print('NO')
    exit(0)
else :
    for _ in range(k) :
        split()
    print('YES')
    print(*(ones + rem))