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 math

n, k = map(int, input().split())

def getMin(n):
    count = 0
    while n:
        count += 1
        d = int(math.log(n, 2))
        n -= math.pow(2, d)
    return count

def getSeq(n, k):
    if n==k:
        return [1]*k
    seq = []
    if k==0:
        return seq
    d = int(math.log(n, 2))
    # print('n,k %s %s'%(n,k))
    for i in range(d, -1, -1):
        # print(i)
        x = int(math.pow(2, i))
        a, b = 1, n-x
        # print('a,b %s %s'%(a,b))
        if a + b < k:
            continue
        else:
            seq += [x]
            seq += getSeq(n-x, k-1)
            return seq
    return seq

def sol(n, k):
    MAX = n
    MIN = getMin(n)
    if k>MAX or k<MIN:
        return "NO"
    else:
        seq = getSeq(n, k)
        seq_new = [str(x) for x in seq]
        return "YES\n%s"%(' '.join(seq_new))

print(sol(n, k))