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 PYTHON):

Solution:
from heapq import heappush as push, heappop as pop

n, k = map(int, raw_input().strip().split())

p = []
for i in xrange(33):
    powi = 1 << i
    x = n & powi
    if x: push(p, -powi)

if k < len(p):
    print "NO"
    exit()

l = len(p)
while k > l:
    v = -pop(p); l -= 1
    if v == 1:
        print "NO"
        exit()
    else:
        s1 = s2 = -(v >> 1)
        push(p, s1)
        push(p, s2)

        l += 2
        
print "YES"
for i in xrange(len(p)):
    p[i] = str(-p[i])

print ' '.join(p)