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:

ni, k = (map(int, input().split(" ")))
n = ni
a = 0
cont = 0

vetor = [0] * 35
while n:
    vetor[cont] = n % 2
    if vetor[cont]:
        a += 1
    n //= 2
    cont += 1

if ni < k or k < a:
    print("NO")
    exit()

else:
    while cont > 0 and a < k:
        while vetor[cont] and a < k:
            vetor[cont] -= 1
            vetor[cont - 1] += 2
            a += 1
        cont -= 1
    if a > k:
        print("NO")
        exit()
    else:
        print("YES")
        b = 1
        for i in range(32):
            while vetor[i]:
                print(b, end=" ")
                vetor[i] -= 1
            b = b * 2