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 = map(int, input().split())
d = dict()
step = 1
kol = 0

while step <= n:
    d[step] = 0
    step *= 2

if step > n:
    step //= 2

while n != 0:
    i = 0
    stepen = 1
    while stepen <= n:
        stepen *= 2
        i += 1
    if stepen > n:
        stepen //= 2
    d[stepen] += 1
    kol += 1
    n -= stepen

if kol > k:
    print("NO")
    exit()

while kol != k:
    if step == 1:
        print("NO")
        exit()
    if d[step] != 0:
        d[step] -= 1
        d[step // 2] += 2
        kol += 1
    else:
        step //= 2
print("YES")
for i in d:
    if d[i] != 0:
        for j in range(d[i]):
            print(i, end=" ")