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())

a = []
p = 0
c = 0

while n > 1:
    if n % 2 == 1:
        a.append(2**p)
        c += 1
    p += 1
    n = n // 2
if n % 2 == 1:
    a.append(2**p)
    c += 1
flag = True
if c > k:
    flag = False

l = c
ans = []
while c < k and l > 0:
    # print(a)
    # print(c)
    q = a.pop()
    l -= 1
    if q == 1:
        ans.append(q)
    if q // 2 >= 1:
        a.append(q // 2)
        a.append(q // 2)
        c += 1
        l += 2
# print(ans)
# print(a)
if c < k or flag == False:
    print('NO')
else:
    print('YES')
    for i in ans:
        print(i, end=' ')
    a.sort()
    for i in a:
        print(i, end=' ')
    print('')