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 dec_to_bin(n):
    ans = ''
    while n // 2 != 0 or n % 2 != 0:
        ans += str(n % 2)
        n //= 2
    return ans[::-1]


def bin_to_dec(n):
    ans = 0
    length = len(n) - 1
    for _ in range(len(n)):
        ans += int(n[_]) * 2 ** length
        length -= 1
    return ans


a = []
n, k = map(int, input().split())
init = n
n = dec_to_bin(n)
if n.count('1') > k or k > init:
    print('NO')
    exit()
for i in range(len(n)):
    if n[i] == '1':
        a.append('1' + (len(n) - i - 1) * '0')
k -= len(a)
j = 0
ones_cnt = 0
while k > 0:
    if a[0] != '1':
        if bin_to_dec(a[0]) < k:
            for h in range(bin_to_dec(a[0])):
                ones_cnt += 1
                k -= 1
            k += 2
            del a[0]
        else:
            a.append(dec_to_bin(bin_to_dec(a[0]) // 2))
            a.append(dec_to_bin(bin_to_dec(a[0]) // 2))
            del a[0]
    else:
        ones_cnt += 1
        del a[0]
        k += 1
    k -= 1
print('YES')
for _ in range(len(a)):
    print(bin_to_dec(a[_]), end=' ')
if ones_cnt != 0:
    for b in range(ones_cnt):
        print(1, end=' ')