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 read(type = 1):
    if type:
        file = open("input.dat", "r")
        line = list(map(int, file.readline().split()))
        file.close()
    else:
        line = list(map(int, input().strip().split()))
    return line[0], line[1]


def solve(n, k):
    sol = []
    m = n
    p = 1
    while p <= n:
        p *= 2
    p //= 2
    a = []
    while n:
        if p <= n:
            n -= p
            a.append(p)
        p //= 2
    a.sort()
    if k < len(a) or k > m:
        return sol
    b = [m]
    for v in a:
        if len(b):
            b.append(b[-1]-v)
        else:
            b.append(m-v)
    tot = 0
    step = 0
    while k:
        if b[step+1] < k:
            # solve the rest
            v = a[step]
            vk = k - b[step+1]
            while v:
                p = 1
                while p <= vk:
                    p *= 2
                p //= 2
                bit = (v // 2) // p
                if vk == p:
                    if bit:
                        bit *= 2
                    else:
                        bit = 1
                for i in range(p):
                    sol.append(bit)
                    v -= bit
                    k -= 1
                    vk -= 1
            step += 1
        else:
            sol.append(a[step])
            step += 1
            k -= 1
    sol.sort()
    return sol


def write(sol):
    line = ""
    for v in sol:
        line += str(v) + " "
    print(line)


n, k = read(0)
sol = solve(n, k)
if len(sol):
    print("YES")
    write(sol)
else:
    print("NO")