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 = map(int,input().split())
b = list(bin(n)[2:])
c1 = b.count('1')
l = len(b)
if k<c1 or k>n:
    print('NO')
else:
    print('YES')
    d = k-c1
    powers = []
    newp = []
    for i in range(l-1,-1,-1):
        if b[i]=='1':
            powers.append(1<<int(l-1-i))
    while d>0:
        p = powers.pop()
        if p==1:
            newp.append(p)
        else:
            powers.append(p>>1)
            powers.append(p>>1)
            d -= 1
    powers.extend(newp)
    powers.sort()
    print(' '.join(map(str,powers)))