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 break_in_pow2(num, arr):
    divisor = 1
    index = 0
    while(num >= divisor * 2):
        divisor *= 2
        index += 1
    arr[index] += 1
    if (num - divisor > 0):
        break_in_pow2(num - divisor, arr)


line = input().split()
n = int(line[0])
k = int(line[1])
max_k = n
pots = [0] * 31

break_in_pow2(n, pots)

biggest_potency = 0
min_k = 0

for i in range(len(pots)):
    potency = pots[i]
    min_k += potency
    if potency != 0:
        biggest_potency = i

if (k < min_k or k > max_k):
    print('NO')
else:
    print('YES')
    for curr_k in range(min_k, k):
        pots[biggest_potency] -= 1
        pots[biggest_potency - 1] += 2
        if (pots[biggest_potency] == 0):
            biggest_potency -= 1
    
    curr_pot = 1
    for pot in pots:
        for i in range(pot):
            print(curr_pot, end=' ')
        curr_pot *= 2
    print()