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:
N = [int(i) for i in input().split()]
kol = N[1]
number = N[0]
k = 1
arr = []
flag = 1
if kol > number:
    flag = 0
elif kol == number:
    flag = 2
else:
    while number != 0:
        while k <= number:
            k *= 2
        k /= 2
        number -= k
        arr.append(int(k))
        k = 1
        
    our_kol = len(arr)
    if our_kol > kol:
        flag = 0
    else:
        while our_kol != kol:
            if kol - our_kol >= arr[0]:
                our_kol += arr[0] - 1
                arr += [1] * arr[0]
                arr.pop(0)
            else:
                d = arr[0] // 2
                arr.pop(0)
                arr.insert(0, d)
                arr.insert(0, d)
                our_kol += 1

if flag == 0:
    print("NO")
elif flag == 2:
    print("YES")
    for i in range(kol):
        print(1, end = " ")
elif flag == 1:
    print("YES")
    for i in arr:
        print(i, end = " ")