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 sys
from collections import deque
input = sys.stdin.readline

n,k=map(int,input().split())

A=[2**i for i in range(31)]
A.reverse()

if n<k:
    print("NO")
    sys.exit()

LIST=[]
for i in range(31):
    if A[i]<=n:
        LIST.append(A[i])
        n-=A[i]

#print(LIST)
SUM=len(LIST)
if SUM>k:
    print("NO")
    sys.exit()
Q = deque(LIST)
#print(Q)
i=0
while SUM!=k:
    if Q[0]==1:
        print("NO")
        break
    elif Q[0]==2:
        Q.popleft()
        Q.append(1)
        Q.append(1)
        SUM+=1
    else:
        x=Q[0]//2
        Q.popleft()
        Q.appendleft(x)
        Q.appendleft(x)
        SUM+=1

else:
    print("YES")
    for l in Q:
        print(l,end=" ")