Refrain#2469

Refrain

1 second
64 megabytes
Hard

Consider a sequence of integers ranging from to . A subsequence of consecutive integers is called a refrain if the product of its length and the number of times it appears in the sequence is maximized.

Find the refrain of the given sequence.

Input

The first line contains two integers and (1 \leq n \leq 150,000, 1 \leq m \leq 10). The second line contains integers from to .

Output

The first line should contain the product of the length of the refrain and the number of its occurrences. The second line should contain the length of the refrain. The third line should contain the refrain subsequence.

Examples

Example 1

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