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 os,io
input = io.BytesIO(os.read(0,os.fstat(0).st_size)).readline
def bincalc(n):
    s = []
    v = 0
    while n:
        r = n%2
        s.append(r)
        n//=2
        v+=r
    return s[::-1],v

n,k = list(map(int,input().split()))
a,v = bincalc(n)
if v>k or k>n:
    print("NO")
else:
    print("YES")
    c = v
    i = 0
    while c<k:
        if a[i]>0:
            a[i]-=1
            a[i+1]+=2
            c+=1
        else:
            i+=1
    out = []
    a = a[::-1]
    for i in range(len(a)):
        out.extend([2**i]*a[i])
    print(*out)