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 decimalToBinary(n):
    bits = []

    bits.append(0 if n % 2 == 0 else 1)
    while n > 1:
        n = n // 2
        bits.append(0 if n % 2 == 0 else 1)
    return bits


n, k = map(int, input().split())
bits = decimalToBinary(n)
i = 0
arr = []
for r in bits:
    if r == 1:
        arr.append(pow(2, i))
    i += 1
cnt = len(arr)
if cnt > k:
    print('NO')
else:
    ones = []
    while cnt < k and len(arr) > 0:
        z = arr[0]
        del arr[0]

        if z > 1:
            half = z // 2
            arr.append(half)
            arr.append(half)

            cnt += 1
        else:
            ones.append(1)

    if cnt < k:
        print('NO')
    else:
        print('YES')
        for o in ones:
            arr.append(o)
        arr.sort()
        for i in arr:
            print(i, end=' ')