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()]

def reversebinary(n):
    L = []
    while n != 0:
        L.append(n%2)
        n = n//2
    return L
def split(exp,pieces):
    if pieces == 1:
        return [exp]
    else:
        return split(exp-1,pieces//2)+split(exp-1,pieces-(pieces//2))
R = reversebinary(n)
low = sum(R)
if (k <= n and k >= low):
    print('YES')
    digits = []
    for i in range(0,len(R)):
        if R[i] == 1:
            digits.append(i)
    s = 0
    c = 0
    while s-c < k-low:
        s += 2**digits[c]
        c += 1
    if c > 0:
        c -= 1
    if s-c == k-low:
        print('1 '*(k-low), end = '')
        for j in range(c,len(digits)):
            print(2**digits[j], end = ' ')
    else:
        s -= 2**digits[c]
        remaining = k-low-s+c
        print('1 '*s, end = '')
        for el in split(digits[c],remaining+1):
            print(2**el, end = ' ')
        if c+1 <= len(digits):
            for j in range(c+1,len(digits)):
                print(2**digits[j], end = ' ')
            
else:
    print('NO')