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:
n, k = map(int, input().split())
A = []
PoT = []

for i in range(35):
	temp = 2**i
	if n >= temp:
		A.append(0)
		PoT.append(2**i)

lenPoT = len(PoT)

temp_k = 0
temp_n = n
IsMAX = True
for i in range(1,lenPoT+1):
	temp_PoT = PoT[lenPoT - i]
	while temp_n >= temp_PoT:
		temp_n -= temp_PoT
		A[lenPoT - i] += 1
		temp_k += 1
		if IsMAX:
			IndMAX = lenPoT - i
			IsMAX = False

FLAG = True

if temp_k > k:
	FLAG = False
elif temp_k == k:
	FLAG = True
else:
	while temp_k < k:
		if IndMAX >= 1:
			if A[IndMAX] == 0:
				IndMAX -= 1
			else:
				A[IndMAX] -= 1
				A[IndMAX - 1] += 2
				temp_k += 1
		else:
			FLAG = False
			break

len_A = len(A)

if FLAG:
	print("YES")
	for i,a in enumerate(A):
		for b in range(a):
			print(2**i, end="")
			if i != len_A - 1 or b != a - 1:
				print(" ", end="")
	print()
else:
	print("NO")