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, k = [int(x) for x in input().split()]
b = bin(n)[2:][::-1]
if (b.count("1") > k or k > n):
    print("NO")
else:
    nums = []
    ans = ""
    for i in range(len(b)):
        if (b[i] == "1"):
            nums.append(2 ** i)
    _k = 0
    while _k + len(nums) < k:
        num = nums.pop()
        if num == 1:
            ans += "1 "
            _k += 1
        else:
            num = num // 2
            nums.append(num)
            nums.append(num)
    for n in nums:
        ans += str(n) + " "
    print("YES")
    print(ans[:len(ans)-1])