Minimum Tree Sequence

You are given a list of integers representing different types of trees along a line. There are n types of trees which are labeled from 1 to n. Your task is to find the length of the smallest contiguous subsequence that contains all n distinct tree types. If such a subsequence does not exist, output INF.

Formally, given an array (trees) of length (m) and an integer (n), find the minimum length (L) such that there exists an index (i) with (1 \leq i \leq m-L+1) for which the subarray (trees[i], trees[i+1], \dots, trees[i+L-1]) contains every integer from (1) to (n) at least once. If no such subsequence exists, output INF.

inputFormat

The input is read from standard input (stdin) and consists of two lines. The first line contains two space-separated integers: (m) (the number of trees) and (n) (the total number of tree types). The second line contains (m) space-separated integers, representing the array (trees).

outputFormat

Output a single line to standard output (stdout) containing the length of the smallest contiguous subsequence that includes all tree types from 1 to (n). If no such subsequence exists, output INF.## sample

12 5
1 2 1 3 2 1 5 1 3 2 4 5

5