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 = (int(i) for i in input().split())

p = 0
nD = n
d_arr = []
while nD > 0:
    if nD % 2 == 1:
        d_arr.append(2 ** p)
    nD = nD // 2
    p += 1
#print(d_arr)

flag = False

ones = 0
for i in d_arr:
    if i == 1:
        ones += 1
    else:
        break

while not flag:
    if len(d_arr) == k:
        print('YES')
        print(' '.join(str(i) for i in d_arr))
        break
    if len(d_arr) > k:
        flag = True
    if len(d_arr) < k:
        if (d_arr[-1] == 1):
            flag = True
            continue
        diff = k  - len(d_arr)
        


        n_d_arr = [1] * ones
        i = ones
        while diff > 0 and i < len(d_arr):
            n_d_arr.append(d_arr[i] // 2)
            n_d_arr.append(d_arr[i] // 2)
            if d_arr[i] // 2 == 1:
                ones += 2
            
            i += 1
            diff -= 1
        
        if i == len(d_arr):
            tail = []
        else:
            tail = d_arr[i:]

        d_arr = n_d_arr + tail
#        print(d_arr)
 #       print("ones: ", ones)

if flag:
    print('NO')