Hey! I have an awesome task with chameleons, 5^th task for Saturday's competition.

Go ahead…

(…)

That's too difficult, I have an easier one, they won't even solve that one.

You are given an array of ~N~ integers from the interval ~[1, K]~. You need to process ~M~ queries. The first type of query requires you to change a number in the array to a different value, and the second type of query requires you to determine the length of the shortest contiguous subarray of the current array that contains all numbers from ~1~ to ~K~.

Hm, I can do it in ~\mathcal O(N^6)~. What's the limit for ~N~?

Input Specification

The first line of input contains the integers ~N~, ~K~ and ~M~ ~(1 \le N, M \le 100\,000, 1 \le K \le 50)~. The second line of input contains ~N~ integers separated by space, the integers from the array. After that, ~M~ queries follow, each in one of the following two forms:

• 1 p v - change the value of the ~p^{th}~ number into ~v~ ~(1 \le p \le N, 1 \le v \le K)~
• 2 - what is the length of the shortest contiguous subarray of the array containing all the integers from ~1~ to ~K~

In test cases worth 30% of total points, it will hold ~1 \le N, M \le 5\,000~.

Output Specification

The output must consist of the answers to the queries of the second type, each in its own line.

If the required subarray doesn't exist, output -1.

Sample Input 1

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

Sample Output 1

3
-1
4

Sample Input 2

6 3 6
1 2 3 2 1 1
2
1 2 1
2
1 4 1
1 6 2
2

Sample Output 2

3
3
4