Get Max Rating (Bitwise AND Subset)

Perform at most k operations, each adding 1 to any rating. After the changes, choose exactly m items and maximize their bitwise AND.

输入格式

The first line contains n k m (1≤m≤n≤100000, 1≤k≤10⁹); the second line contains n rating values (1..10⁹).

输出格式

Output a single integer answer.

样例 1

输入：

2 2 2
1 2

输出：

2

样例 2

输入：

1 3 1
5

输出：

8

样例 3

输入：

3 2 3
1 1 1

输出：

1

样例说明

Example 1: raise 1 to 2 and choose two items, giving an AND of 2; bringing both items to 3 takes 3 operations, which exceeds the budget. Example 2: the only value goes from 5 to 8, so the answer is 8. Example 3: bringing all three items to 2 takes 3 operations but the budget is only 2, so the maximum AND stays 1.