pog loves szh II

Time Limit: 4000/2000 MS (Java/Others)

Memory Limit: 65536/65536 K (Java/Others)

Description

Pog and Szh are playing games.There is a sequence with $n$ numbers, Pog will choose a number A from the sequence. Szh will choose an another number named B from the rest in the sequence. Then the score will be $(A+B)$ mod $p$.They hope to get the largest score.And what is the largest score?

Input

Several groups of data (no more than $5$ groups,$n \geq 1000$).

For each case:

The following line contains two integers,$n(2 \leq n \leq 100000)$,$p(1 \leq p \leq 2^{31}-1)$。

The following line contains $n$ integers $a_i(0 \leq a_i \leq 2^{31}-1)$。

Output

For each case,output an integer means the largest score.

Sample Input

4 4 1 2 3 0 4 4 0 0 2 2

Sample Output

3 2

Hint

hujie

Source

BestCoder Round #43

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