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 = [int(i) for i in input().split()]
a = [0] * 33
c = 0
for i in range(33):
    if (n >> i) & 1 == 1:
        a[i] += 1
        c += 1

if c > k:
    print("NO")
else:
    pos = 32
    while c < k and pos > 0:
        if a[pos] == 0:
            pos -= 1
            continue
        c += 1
        a[pos] -= 1
        a[pos - 1] += 2
    if c != k:
        print("NO")
    else:
        print("YES")
        for i in range(33):
            for j in range(a[i]):
                print(1 << i, end=" ")