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:
from collections import deque, Counter, OrderedDict
from heapq import nsmallest, nlargest
from math import ceil,floor,log,log2,sqrt,gcd,factorial
def binNumber(n,size=1):
    return bin(n)[2:].zfill(size)

def iar():
    return list(map(int,input().split()))

def ini():
    return int(input())

def isp():
    return map(int,input().split())

def sti():
    return str(input())


class pair:
    def __init__(self,f,s):
        self.fi = f
        self.se = s
    def __lt__(self,other):
        return (self.fi,self.se) < (other.fi,other.se)

#  =========     /\       /|    |====/|
#      |        /  \       |    |   / |
#      |       /____\      |    |  /  |
#      |      /      \     |    | /   |
#  ========= /        \  =====  |/====|  
#  code

if __name__ == "__main__":
    n,k = isp()
    m = floor(log2(n))
    rem = n%(2**m)
    a = [2**m]
    while m >= 0:
        m -= 1
        if rem//(2**m) > 0:
            a.append(2**m)
        rem = rem%(2**m)
    #print(a)
    if len(a) > k or n < k:
        print('NO')
        quit()
    i = 0
    while len(a) != k:
        while a[i] == 1:
            i += 1
        a[i]//=2
        a.insert(i,a[i])
    print('YES')
    print(' '.join(list(map(str,a))))