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 libraries for input/ output handling 
# on generic level 
import sys 

# use this for interactive problems
def fprint(x):
    print(x, flush=True)
  
# using this print for fast
def qprint(x):
    sys.stdout.write(str(x) + "\n")
  
# using this input
def input():
    return sys.stdin.readline()
  
##################################### 
# code below
N,K = map(int, input().split())
n_bits = format(N, "b")
n_bits = str(n_bits)
num_1s = n_bits.count("1")
# print(n_bits)
print_list = []
if K < num_1s:
        print("NO")

elif K > N:
        print("NO")
else:
        print("YES")
        for index, ele in enumerate(n_bits):
                if ele == "1":
                        print_list.append(2**(len(n_bits)-index-1))

        while(len(print_list)!=K):
                if(print_list[0]==1):
                        print(print_list.pop(0),end=" ")
                        K -= 1
                else:
                        element = print_list.pop(0)
                        print_list.append(int(element/2))
                        print_list.append(int(element/2))

        print(" ".join(map(str, print_list)))