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:
import sys
n, k = map(int, input().split())
m = bin(n)[2:]
m = [int(i) for i in m]

def val(a):
    l = len(a)
    x = 0
    p = 1
    for i in range(l):
        x += a[i] * p
        p *= 2
    return x

while True:
    if sum(m) == k:
        print("YES")
        m = m[::-1]
        x = 1
        for i in m:
            for j in range(i):
                print(x, end=' ')
            x *= 2
        print()
        sys.exit(0)
    else:
        l = len(m)
        f = 0
        x = sum(m)
        for i in range(l - 1):
            while m[i] > 0:
                m[i] -= 1
                m[i + 1] += 2
                f = 1
                x += 1
                if x == k:
                    break
            if x == k:
                break
        if f == 0:
            print("NO")
            sys.exit(0)