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:
# https://codeforces.com/contest/1095/problem/C

# k > n , no
# divide n into a series of power of two, keep dividing the biggest power of two until k or reach 1.


def main():
    a = input()
    n, k = [int(i) for i in a.split(' ')]
    if k > n:
        print("NO")
        return

    c = [0]*30
    cnt = 0
    for i in range(30):
        if n & 1 << i != 0:
            c[i] += 1
            cnt += 1
    if cnt > k:
        print("NO")
        return
    print("YES")
    k -= cnt
    for i in range(29, 0, -1):
        while k > 0 and c[i] > 0:
            k -= 1
            c[i] -= 1
            c[i-1] += 2
    res = ''
    for i in range(29, -1, -1):
        while c[i] > 0:
            c[i] -= 1
            res += str(1 << i) + ' '
    print(res)


main()