AT_abc440_e [ABC440E] Cookies

There are $ 10^{100} $ cookies of each of $ N $ types. The deliciousness per cookie of the $ i $ -th type is $ A_i $ . You will choose a total of $ K $ cookies from these. Two ways of choosing cookies are considered the same if and only if the multisets of types of chosen cookies match. For each of the $ \binom{N+K-1}{K} $ ways of choosing, consider the sum of deliciousness of the chosen cookies. Let $ S_1,S_2,\dots $ be these sums in descending order, with duplicates included. Find $ S_1,\dots,S_X $ .

The input is given from Standard Input in the following format: > $ N $ $ K $ $ X $ $ A_1 $ $ \dots $ $ A_N $

Let $ S_1,S_2,\dots $ be the possible sums of deliciousness of the chosen $ K $ cookies in descending order, with duplicates included. Output $ S_1,\dots,S_X $ in this order, separated by newlines.

### Sample Explanation 1 There are $ 5 $ ways to choose $ 4 $ cookies: " $ k $ cookies of type $ 1 $ and $ 4-k $ cookies of type $ 2 $ " $ (0\leq k \leq 4) $ , where the sums of deliciousness of the chosen cookies are $ 80,70,60,50,40 $ . ### Sample Explanation 2 Different ways of choosing cookies may result in the same sum of deliciousness. ### Constraints - $ 1\leq N \leq 50 $ - $ 1 \leq K \leq 10^5 $ - $ 1 \leq X \leq \min\left(10^5, \binom{N+K-1}{K}\right) $ - $ -10^9 \leq A_i \leq 10^9 $ - All input values are integers.