Swimming Competition

In Bitlandia, every pupil may take part in an open swimming competition. Registering in advance is not required, so the organisers never know beforehand how many pupils will show up.

This year the number of participating pupils is smaller than the number of swimlanes in Bitlandia, which is 500 000. The organisers decide to split the participants into smaller groups, each holding at least $A$ and at most $B$ participants.

To make the competition as fun as possible, the organisers also want the swimmers in each group to have speeds that are as similar as possible.

Write a program that divides the swimmers into groups so that the maximum, taken over all groups, of the absolute difference between the times of the slowest and the fastest swimmer in a group is as small as possible.

The first line contains three integers: the number of participants $N$, and the minimum $A$ and maximum $B$ number of swimmers allowed in each group.

Each of the next $N$ lines contains one time $t_i$, the time a swimmer needs to complete the distance.

The input is always such that a valid division exists.

Print a single integer: the smallest possible value of the maximum, over all groups, of the difference between the times of the slowest and the fastest swimmer.

• $2 \le N \le 1\,000\,000$
• $2 \le A \le B \le 500\,000$
• $1 \le t_i \le 1\,000\,000$ for every $i$