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 sys import stdin
#n=int(stdin.readline().strip())
n,m=map(int,stdin.readline().strip().split())
#s=list(map(int,stdin.readline().strip().split()))
p=[0 for i in range(30)]
s=bin(n)[::-1]
x=0
for i in range(len(s)):
    if s[i]=="1":
        p[i]=1
        x+=1
if x>m:
    print("NO")
    exit(0)
y=29
while y>0 and x!=m:
    if p[y]>0:
        x+=1
        p[y]-=1
        p[y-1]+=2
    else:
        y-=1
if x==m:
    print("YES")
    ans=[]
    for i in range(len(p)):
        for j in range(p[i]):
            ans.append(2**i)
    print(*ans)
else:
    print("NO")