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,m = map(int,input().split())
b = bin(n)[2:]
j = b.count("1")
if j<=m<=n :
    print("YES")
else :
    exit(print("NO"))
heap=[]
t=0
for i in b[::-1] :
    if i=="1" :
        heap.append(int(2**t))
    t+=1
heap.sort()
p=0
if heap[0]==1:
    heap=heap[1:]
    m=m-1
    p=1

while (len(heap))!=m :
    #print(heap)
    while (len(heap))!=m and heap[-1]!=1 :
        #print(heap,m)
        t=heap.pop()
        t=t//2
        if t==1 :
            m=m-2
            p=p+2
        else :
           heap = heap + [t] +[t]
heap+=[1]*p
print(*heap)