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 base2(n):
    n = int(n)
    res = ''
    while(n>0):
        res += str(n%2)
        n = n//2
    return res[::-1]
t, k = input().split()
n = str(base2(t))
if (int(t)<int(k) or int(k)<n.count('1')): print('NO')
else:
    k = int(k)
    lis = []
    for i in range(len(n)):
        lis.append(int(n[i]))
    lis.reverse()
    while(sum(lis)<k):
        for i in range(len(lis)-1,0,-1):
            if lis[i] != 0: 
                if sum(lis)+lis[i] < k:
                    lis[i-1] += 2*lis[i]
                    lis[i] = 0
                else:
                    t = k - sum(lis)
                    lis[i-1] += t*2
                    lis[i] -= t
    print('YES')
    for i in range(len(lis)):
        print(lis[i] * (str(2**i)+' '), end = '')