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:
n,k=[int(x) for x in input().split()]
ans=[]
power=[]
for i in range(0,34):
    power.append(2**i)
flag=0
temp=0
m=n
prev=temp
while True:
    temp=0
    k-=1
    for i in power:
        temp=i
        if (m-temp)<(k):
            temp=prev
            break
        prev=temp
    m-=temp
    ans.append(temp)
    if temp==0:
        flag=1
    if m==0 or k==0:
        break
    
if flag==1 or m!=0:
    print("NO")
else:
    print("YES")
    for i in ans:
        print(i,end=" ")
    print()