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()))
potenciasde2 = []
pot2 = 1
while pot2 <= n:
    if pot2 & n:
        potenciasde2.append(pot2)
    pot2 *= 2
if len(potenciasde2) > k or k > n:
    print('NO')
else:
    print('YES')
    while k != len(potenciasde2):
        i = potenciasde2.index(max(potenciasde2))
        maximo = max(potenciasde2)
        m = 1
        while len(potenciasde2)-1 + (potenciasde2[i]//m) > k:
            m *= 2
        del potenciasde2[i]
        potenciasde2 += [m]*(maximo//m)
    print(*potenciasde2)