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 get_bit(n):
    count_shifts = 0

    while (n > 1):
        n = n >> 1
        count_shifts += 1
    
    return pow(2, count_shifts)

str_input = input().split()
array = []
n = int(str_input[0])
k = int(str_input[1])
eh_possivel = True

if (k > n):
    print("NO")
    eh_possivel = False
else:
    if (n % 2 != 0): #numero eh impar, com certeza 1 será printado
        array.append(1)
        n -= 1
        k -= 1

    while (n > 0):
        if (k == 0):
            print("NO")
            eh_possivel = False
            break

        bit_mais_sig = get_bit(n) # retorna o bit mais significativo de n
        n -= bit_mais_sig
        k -= 1
        array.append(bit_mais_sig)

            
    i = 0
    while(k > 0):
        if (array[i] != 1):
            metade = array[i] // 2
            array[i] = metade
            array.append(metade)
            k -= 1
        else:
            i += 1

    if (eh_possivel):
        print("YES")
        print(" ".join([str(x) for x in array]))