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 max_2_pow(n):
    k = 0
    while n > 0:
        n = n//2
        k += 1
    return 2**(k-1)

n, k = [int(x) for x in input().split(" ")]
l = []
if k <= n:
    if n % 2 != 0:
        l.append(1)
        k-=1
        n-=1

    while n > 0 and k > 0:
        p = max_2_pow(n)
        l.append(p)
        n-=p
        k-=1

    if k == 0 and n > 0:
        print("NO")
    else:
        i = 0
        while k > 0:
            if l[i] != 1:
                h = l[i]//2
                l[i] = h
                l.append(h)
                k-=1
            else:
                i+=1
        print("YES")
        print(" ".join([str(x) for x in l]))

else:
    print("NO")