"Hey! I have an awesome task with chameleons, 5^th task for Saturday’s competition."</p>

"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 O(N⁶). What’s the limit for N?”

입력 형식

The first line of input contains the integers N, K and M (1 ≤ N, M ≤ 100 000, 1 ≤ K ≤ 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:</p>

• “1 p v” - change the value of the p^th number into v (1 ≤ p ≤ N, 1 ≤ v ≤ K)
• “2” - what is the length of the shortest contiguous subarray of the array containing all the integers from 1 to K

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.

예제 입력 1

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

예제 출력 1

3
-1
4

예제 입력 2

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

예제 출력 2

3
3
4