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 = list(map(int,input().split()))

bin_n = bin(n)[2:]

a = []
for i in bin_n:
    a.append(int(i))

l = len(a)
s = sum(a)
if s > k:
    print('NO')
    exit()
if s == k:
    print('YES')
    for i in range(l):
        for j in range(a[i]):
            print(2**(l-i-1), end = ' ')
    exit()

for i in range(l-1):
    while a[i]:
        a[i] -= 1
        a[i+1] += 2
        s += 1
        if s == k:
            print('YES')
            for i in range(l):
                for j in range(a[i]):
                    print(2**(l-i-1), end = ' ')
            exit()

print('NO')