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, m = map(int,input().split())
x = bin(n)[2:]
ones = x.count('1')

if m < ones or m > n :
    print("NO")
else:
    print("YES")
    x = x [::-1]
    s = [ 0 for i in range(35) ]
    for i in range(len(x)):
        if x[i] == '1':
            s[i] += 1

    status = False
    while ones != m:
        if status == True :
            break
        for i in range(1,35):
            if s[i] != 0 :
                s[i] -= 1
                s[i-1] += 2
                ones += 1
            if ones == m :
                status = True
                break
    pow = [ 2**i for i in range(35) ]
    for i in range(0,35):
        for j in range(0,s[i]):
            print(pow[i], end = " ")
    print()