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:
def findYes(arr, m, k, ans):
    ans_string = ""
    print("YES")
    if(ans == k):
        for i in range(m):
            if(arr[i] == 1):
                seq = pow(2, i)
                ans_string += str(seq) + " "
    else:
        p = m - 1
        while(ans != k):
            while(arr[p] >= 1):
                arr[p] -= 1
                arr[p-1] += 2
                ans += 1
                if(ans == k):
                    break
            p -= 1
        i = m - 1
        while(i >= 0):
            if(arr[i] >= 1):
                for j in range(arr[i]):
                    seq2 = pow(2, i)
                    ans_string += str(seq2) + " "
            i -= 1
    return ans_string

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

ans = 0
arr = [0]*1000
m = 0
temp_n = n
while(temp_n):
    arr[m] = temp_n%2
    temp_n //= 2
    m += 1
i = m - 1

while(i >= 0):
    if(arr[i] == 1):
        ans += 1
    i -= 1

if(k > n or k < ans):
    print("NO")
else:
    ans_string = findYes(arr, m, k, ans)
    print(ans_string)