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 = input().split(" ")
n = int(n) #<= 10**9
k = int(k) #<= 2*10**5

s = format(n, 'b')
s = list(s)
s = map(int, s)
s = list(s)
s = s[::-1]

m = sum(s)

if k == m:
    print("YES")
    i = 0
    while i < len(s):
        if s[i]:
            print(2**i, end=" ")
        i += 1
    print()
elif k == n:
    print("YES")
    print('1 '*k)
    print()
elif k > m and k < n:
    delta = k-m
    i = len(s)-1
    while delta > 0:
        if s[i] > 0:
            s[i] -= 1
            s[i-1] += 2
            delta -= 1
        elif s[i] == 0:
            i -= 1
    print("YES")
    i = 0
    b = 1
    while i < len(s):
        if s[i] > 0:
            print(b, end=" ")
            s[i] -= 1
            delta -= 1
        if s[i] == 0:
            i += 1
            b *= 2
    print()
else:
    print("NO")