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())
if k>n:
    print("NO")
elif k==n:
    print("YES")
    for i in range(n):
        print("1", end=" ")
    print()
else:
    pows = [0]*30
    l = i = 0
    nc = n
    while nc>0:
        pows[i]=nc%2
        l+=pows[i]
        nc//=2
        i+=1
    if k<l:
        print("NO")
    else:
        for i in range(29, 0, -1):
            if l<k:
                while pows[i]>0 and l<k:
                    pows[i]-=1
                    pows[i-1]+=2
                    l+=1
            else:
                break
        m=1
        print("YES")
        for i in range(30):
            for j in range(pows[i]):
                print(m, end=" ")
            m*=2
        print()