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 = list(map(int, input().split()))
n = bin(n)[2:]
cont = 0
for i in n:
    if i == '1':
        cont += 1
    
n = list(map(int, n))
k -= cont
while k > 0:
    for i in range(len(n)):
        if n[i] != 0:
            if i+1 >= len(n):
                print("NO")
                exit(0)
            else:
                n[i+1]+=2
                n[i] -= 1
                k-=1
                break
if k == 0:
    print("YES")
    res = ""
    cont = 0
    for i in range(len(n)-1, -1, -1):
        res = res + (str(2**cont) + ' ')*n[i]
        cont += 1
    print(res)
else:
    print("NO")