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 PYTHON):

Solution:
def FindAllElements(n, k):
    sum = k

    A = [1 for i in range(k)]
    i = k - 1
    while(i >= 0):

        while (sum + A[i] <= n):

            sum += A[i]
            A[i] *= 2
        i -= 1

    if (sum != n):
        print("NO")

    else:
        str_=""
        for i in range(0, k, 1):
            str_ += str(A[i]) + ' '
        print 'YES'
        print str_


inpu = raw_input().split()
n, k = int(inpu[0]), int(inpu[1])
FindAllElements(n, k)