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:
import heapq
n,k=map(int,input().split())
def popcount(n):
    c=0
    for i in range(32):
        if n&(1<<i):
            c+=1
            b.append(-i)
    return c
b=[]
summand=popcount(n)
ans=[]
if summand > k or k > n:
    print('NO')
else:
    b.reverse()
    while len(b) < k:
        a=heapq.heappop(b)
        heapq.heappush(b,a+1)
        heapq.heappush(b,a+1)


    for i in b:
        ans.append(1<<-i)
    print('YES')
    print(*ans)