K Subset Sums II

You are given an array of n integers. Consider the sums of all \binom{n}{m} subsets of the given array with exactly m elements. Your task is to find the k smallest subset sums.

Input

The first line has three integers n, m and k: the size of the array, the size of the subsets and the number of subset sums k. The next line has n integers x_1, x_2,\dots, x_n: the contents of the array.

Output

Print k integers: the k smallest subset sums in increasing order.

Constraints

1 \le m < n \le 2 \cdot 10^5

$1 \le k \le \min\left(\binom{n}{m}, 2 \cdot 10^5\right)$

$-10^9 \le x_i \le 10^9$

Example

Input

5 3 9
-3 1 5 2 0

Output

-2 -1 0 2 3 3 4 6 7