Maximum sum subset - MarisaOJ: Marisa Online Judge

Maximum sum subset

Time limit: 1000 ms
Memory limit: 256 MB
Given an array $A$ of $n$ integers. Find a subset of $A$ so that its sum modulo $10^9$ is maximum. In other words, find $k \le n$ indices $i_1, i_2,...,i_k$ so that: $$A_{i_1} + A_{i_2} + ... + A_{i_k} \mod 10^9$$ is maximum. ### Input - The first line contains an integer $n$. - The second line contains $n$ integers $A_i$. ### Output - Prin the maximum value of $A_{i_1} + A_{i_2} + ... + A_{i_k} \mod 10^9$. ### Constraints - $1 \le n \le 40$. - $1 \le A_i \le 10^9$. ### Example Input: ``` 3 1000000000 1000000000 6 ``` Output: ``` 6 ```