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 mi():
    return map(int, input().split(' '))

n , k = mi()
s = bin(n)[2:]

ub = 0
for i in s:
    if int(i) == 1:
        ub +=1
powers = []
i =1
while i < 10e9 + 7:
    powers.append(i)
    i*=2

ans = [1] * k
if n < k or k < ub:
    print("NO")
else:
    print("YES")
    if sum(ans) == n:
        print(*ans)
    else:
        tsum = sum(ans)
        i = 0
        j = 1
        while(tsum != n):
            ans[i] = powers[j]
            tsum += powers[j] - powers[j-1]
            if tsum == n:
                break
            elif tsum > n:
                ans[i] = powers[j-1]
                tsum -= powers[j] - powers[j-1]
                j = 0
                i+=1
            j+=1

        print(*ans)