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 dec_to_bin(n):
    bin = [];
    while n != 0:
        bin.append(n % 2)
        n = n//2;
    return  bin
n, k = map(int, input().split());
bin = dec_to_bin(n);
su = sum(bin);
if(su > k) or (k > n):
    print("NO");
else:
    pos = len(bin) - 1;
    while True:
        if(su - bin[pos]) + 2 * bin[pos] < k:
            bin[pos-1] += bin[pos] * 2;
            su += bin[pos];
            bin[pos] = 0;
            pos -= 1;
        else:
            d = k - su;
            bin[pos] -= d;
            bin[pos - 1] += 2*d;
            break;
    print("YES")
    for i in range(pos+1):
        for j in range(bin[i]):
            print(2**i, end=' ');