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 countSetBits(n): 
    count = 0
    while (n): 
        count += n & 1
        n >>= 1
    return count

n,k = list(map(int,input().split()))
jj = countSetBits(n)
bi = bin(n)[2:]
a = []
l = len(bi)
# print(bi)
for i,j in enumerate(bi):
    # print(i,j)
    if j=='1':
        a.append(2**(l-1-i))
kk = 0
# print(a)
if(k<jj or k>n):
    print('NO')
else:
    print('YES')
    while(k != len(a)):
        # print(a[kk],end=' ')
        while a[kk]==1:
            kk+=1
        a[kk]= int(a[kk])//2
        a.append(a[kk])

    print(' '.join(list(map(str,a))))