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:
import sys
n, k = map(int, input().split())
l = []
cop = n
t = 0
while(cop > 0):
    x = cop % 2*pow(2, t)
    cop //= 2
    t += 1
    if x != 0:
        l.append(x)
l.sort(reverse=True)
if k > n or k < len(l):
    print("NO")
    sys.exit()
u = len(l)-1
while(len(l) != k):
    if l[u] == 1:
        u -= 1
        if u == -1:
            u += len(l)
    else:
        l[u] = l[u]//2
        l.append(l[u])
    # print(l)
l.sort()
print("YES")
print(*l)
# print(sum(l))