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())

st = []

ones = bin(n).count('1')

if k == 1:
    if ones == 1:
        print("YES")
        print(n)
    else:
        print("NO")

else:
    if ones > k:
        print("NO")
    else:
        po = 0
        bi = bin(n)[2:]
        for i in range(len(bi)-1,-1,-1):
            if bi[i] == '1' and po != 0:
                st.append(2**po)
            po += 1
        st.sort()
        excess = k - ones
        ans = []
        if excess == 0:
            print("YES")
            if n % 2 == 1:
                st.append(1)
            print(' '.join(map(str, st)))
        else:
            if sum(st) < excess:
                print("NO")
            else:
                ans = []
                while excess > 0 and len(st) != 0:
                    curr = st[-1]
                    st.pop()
                    if curr // 2 > 1:
                        st.append(curr//2)
                        st.append(curr//2)
                    excess -= 1

                if excess != 0:
                    print("NO")
                else:
                    ans = [i for i in st]
                    rem = n - sum(ans)

                    for j in range(rem):
                        ans.append(1)

                    print("YES")
                    print(' '.join(map(str, ans)))