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 heapq import heappush as push
from heapq import heappop as pop
n, k = map(int, input().split())
Q = []
i = 0
while n != 0:
    if n & 1: push(Q, -(1<<i))
    i += 1
    n = n>>1
if len(Q) > k:
    print("NO")
else:
    while len(Q) != k:
        x = pop(Q)
        if x == -1:
            print("NO")
            exit()
        push(Q, x//2)
        push(Q, x//2)
    print("YES")
    Q = [-x for x in Q]
    print(*Q)