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:


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




if n<k:
    print 'NO'
    exit()
A=[]
ct=0
while n>0:
    x=n&1
    ct+=x
    A.append(x)
    n=n>>1

if ct>k:
    print 'NO'
    exit()
m=len(A)
i=m-1
while ct<k:
    while ct<k and A[i]>0 and i>0:
        A[i]-=1
        A[i-1]+=2
        ct+=1
    i-=1
#print A
pp=1
print 'YES'
for i in range(m):
    for j in range(A[i]):
        print pp,
    pp*=2

exit()