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=map(int,input().split())
s=bin(n)[2:]
st=[]
if s.count('1') > k or k>n:
    print("NO")
else:
    st=[]
    for i in range(len(s)):
        if int(s[i]):
            st.append(int(s[i])*(2**(len(s)-1-i)))
    #print(st)
    ans=k-len(st)
    st1=[]
    while ans:
        if st[-1]==1:
            st1.append(st.pop())
        else:
            temp=st.pop()
            st.append(temp//2)
            st.append(temp//2)
            ans-=1
    while st:
        st1.append(st.pop())
    print("YES")    
    print(*st1)