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 heapq
n,k=map(int,input().split())
bits=[0]*31
i=0
l=[]
n1=n
while(n>0):
    bits[i]=n&1
    if(bits[i]==1):
        l.append(2**i)
    i+=1
    n>>=1
#print(bits,n,k,l)
if(k>n1 or k<len(l)):
    print("NO")
else:
    length=len(l)
    for i in range(length):
        l[i]*=-1
    heapq.heapify(l)
    for i in range(length,k):
        x=heapq.heappop(l)
        heapq.heappush(l,x//2)
        heapq.heappush(l,x//2)
    print("YES")
    for i in l:
        print(-1*i,end=" ")