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:
from operator import itemgetter
#int(input())
#map(int,input().split())
#[list(map(int,input().split())) for i in range(q)]
#print("YES" * ans + "NO" * (1-ans))
n,k = map(int,input().split())
num = bin(n)[2:]
num1 = num.count("1")
if num1 > k or k > n:
    print("NO")
else:
    num2 = len(num)
    ai = [0] * num2
    for i in range(num2):
        ai[i] = int(num[i])
    i = 0
    while k > num1:
        ai[i] -= 1
        ai[i+1] += 2
        if ai[i] == 0:
            i += 1
        num1 += 1
    print("YES")
    x = 1
    for i in range(num2-1,-1,-1):
        print((str(x)+" ") * ai[i],end="")
        x <<= 1