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:
# python rough_work.py < in > out && cat out && diff -qs out check
# n = int(input())
import math
n, k = [int(var) for var in input().split()]
# n, k = 9, 4

maxOnes = 0
powers, power = [1], int(math.log2(n))

for i in range(power+1):
    if n & 1 << i: maxOnes += 1 

for i in range(power):
    powers.append(powers[-1]*2)

# print(powers)
if not(maxOnes <= k <= n):
    print('NO')
else:
    print("YES")
    while k != 0:
        if k==n :
            for _ in range(k):
                print(1, end = " ")
            
            k, n = 0, 0
        else:
            for Idx in reversed(range(1+int(math.log2(n)))):
                if k - 1 <= n - powers[Idx]:
                    k -= 1
                    n -= powers[Idx]
                    print(powers[Idx], end = " ")
                    break
    print()