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 = list(map(int, input().split()))
n = N
mas = [1] * 32
ans = [0] * 32
for i in range(1, 32):
    mas[i] = mas[i - 1] * 2
I = 31
while n > 0:
    if n >= mas[I]:
        ans[I] += 1
        n -= mas[I]
    I -= 1
if sum(ans) > k or k > N:
    print("NO")
else:
    print("YES")
    k -= sum(ans)
    while k > 0:
        for i in range(31, 0, -1):
            if ans[i] > 0:
                ans[i] -= 1
                ans[i - 1] += 2
                k -= 1
                break
    for i in range(31, -1, -1):
        for j in range(ans[i]):
            print(mas[i], end=' ')