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:
# cook your dish here

# from math import factorial, ceil, pow, sqrt, floor, gcd
from sys import stdin, stdout

# from collections import defaultdict, Counter, deque
# from bisect import bisect_left, bisect_right
# import sympy
# from itertools import permutations
# import numpy as np

#           n = int(stdin.readline())
#           stdout.write(str())
#           s = stdin.readline().strip('\n')
#           map(int, stdin.readline().split())
#           l = list(map(int, stdin.readline().split()))


a, b = map(int, stdin.readline().split())
shan = [1]*b
a -= b
i = 0
while i < b and a:
    while shan[i] <= a:
        a -= shan[i]
        shan[i] *= 2
    i+=1
if a:
    print("NO")
else:
    print("YES")
    print(*shan)