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 = map(int, input().split())
m = bin(n)
m = m[2:]
if (m.count('1') > k):
    print("NO")
elif (m.count('1') == k):
    print("YES")
    for i in range(len(m)):
        if (m[i] == '1'):
            print(2 ** (len(m) - 1 - i), end = ' ')  
else:
    a = [0] * (len(m) + 1)
    for i in range(len(m)):
        a[i] = int(m[len(m) - i - 1])
    cnt = m.count('1')
    for i in range(len(a) - 1, 0, -1):
        l = min(a[i], k - cnt)
        cnt += l
        a[i - 1] += 2 * l
        a[i] -= l
    if (cnt < k):
        print("NO")
    else:
        print("YES")
        for i in range(len(a)):
            while (a[i] > 0):
                print(2 ** i, end = ' ')
                a[i] -= 1