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:
bits = 0
n,k = map(int,input().split())
maxbits = 0
a = []
for bit in range(0,30):
    if n & (1 << bit):
        bits += 1
        maxbits += 2 ** bit
        a.append(1)
    else:
        a.append(0)

if bits > k or maxbits < k:
    print("NO")
    exit()
a = a[::-1]

for i in range(29):
    if a[i] == 0:
        continue
    diff = k - bits
    a[i+1] += min(diff,a[i]) * 2
    bits += min(diff,a[i])
    a[i] -= min(diff,a[i])
print("YES")

a = a[::-1]

for i in range(30):
    if a[i]:
        for j in range(a[i]):
            print(2**i,end=" ")