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:
import sys
n, k = [int(s) for s in input().split()]
copy_n = n
counter = 1
while 2 ** counter < n:
    counter += 1
if 2 ** counter != n:
    counter -= 1
n -= 2 ** counter
array = [0] * (counter + 1)
array[counter] = 1
for i in range(len(array) - 1, -1, -1):
    if n >= 2 ** i:
        array[i] += 1
        n -= 2 ** i
#print(array)
if sum(array) > k or copy_n // k == 0:
    print('NO')
    sys.exit(0)
print('YES')
diff = k - sum(array)
while diff != 0:
    array[counter - 1] += 2
    array[counter] -= 1
    if array[counter] == 0:
        counter -= 1
    diff -= 1
#print(array)
answer = []
for i in range(len(array)):
    for j in range(array[i]):
        answer.append(str(2 ** i))
print(' '.join(answer))
#print([str(2 ** i) for j in range(array[i] + 1) for i in range(len(array))])