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 PYTHON):

Solution:
import math
def main():

    cont = raw_input()
    list = cont.strip('\n').split(' ')
    num = int(list[0])
    k = int(list[1])
    power = []
    if k > num:
        print("NO")
    else:
        while num != 0:
            power.append(int(num%2))
            num = int(num/2)
        cont = power.count(1)
        if cont > k:
            print("NO")
        else:
            print("YES")
            dif = k - cont
            while dif != 0:
                aux = power.pop()
                if aux != 0:
                    if aux < dif:
                        power[len(power)-1] = power[len(power)-1] + 2*aux
                        dif = dif - aux
                    else:
                        aux = aux - dif
                        power[len(power)-1] = power[len(power)-1] + 2*dif
                        dif = 0
                        power.append(aux)
            for i in range(len(power)):
                for j in range(power[i]):
                    print pow(2, i),

main();