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 bits(n):
    arr = []
    i = 0
    while n>0:
        a = n&1
        if a == 1:
            arr.append(2**i)
        i += 1
        n = n >> 1
    return arr

def check(n,k):
    if k > n:
        print('NO')
        return
    arr = bits(n)
    i = 0
    while i<=len(arr):
        if len(arr) == k:
            print('YES')
            for i in arr:
                print(i,end=' ')
            break
        elif len(arr)>k:
            print('NO')
            break
        if arr[i] == 1:
            i += 1
        else:
            x = arr[i]
            arr[i] = arr[i]//2
            x = x//2
            arr.append(x)
n,k = [int(x) for x in input().split()]
check(n,k)