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 print_arr(arr,maxi):
    for i in range(40):
        if arr[i] != 0:
            if i != maxi:
                for j in range(arr[i]):
                    print(2**i,end=" ")
            else:
                for j in range(arr[i]-1):
                    print(2**i,end=" ")
                print(2**i)


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

tmp = n

arr = [0 for _ in range(40)]
count = 0
maxi = 0
for i in range(40)[::-1]:
    if tmp >= 2**i:
        arr[i] += 1
        tmp -= 2**i
        count += 1
        if maxi < i:
            maxi = i
if k < count or n < k:
    print('NO')
elif k == count:
    print('YES')
    print_arr(arr,maxi)
else:
    while(k!=count):
        if count + arr[maxi] <= k:
            count += arr[maxi]
            arr[maxi-1] += 2*arr[maxi]
            arr[maxi] = 0
            maxi -= 1
        elif k < count + arr[maxi]:
            temp = k - count
            arr[maxi] -= temp
            arr[maxi-1] += 2*temp
            count = k
    print('YES') 
    print_arr(arr,maxi)