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:
def mlt(): return map(int, input().split())


x, y = mlt()
if x == y:
    print('YES')
    print('1 '*x)
    exit(0)
s = []
pw = 0
v = x
while x:
    if x % 2:
        s.append(1 << pw)
    pw += 1
    x //= 2

if y > v or y < len(s):
    print('NO')
    exit(0)

res = []
s.reverse()
cur = -1
n = 0
while n < len(s):
    if s[n] > y:
        break
    if s[n] <= y:
        rem = len(s)-n-1
        if rem+s[n] >= y:

            cur = s[n]
            break
        else:
            y -= s[n]
            res += [1]*s[n]
            n += 1

cr = [s[n]]
y -= len(s[n+1:])+1
res += s[n+1:]
ind = 0
tm = y
while y:
    cur = cr[ind]
    cr.append(cur//2)
    cr.append(cur//2)
    y -= 1
    ind += 1
cr.reverse()
res += cr[:tm+1]
print('YES')
print(*res)