Nekameleoni

“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 $\mathrm{O}(N^6)$. What’s the limit for $N$?”

Input

The first line of input contains the integers $N$, $K$ and $M$ ($1 \leq N, M \leq 100\, 000$, $1 \leq K \leq 50$). 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 $v$ ($1 \leq p \leq N, 1 \leq v \leq K$)

  • “2”—what is the length of the shortest contiguous subarray of the array containing all the integers from $1$ to $K$.

Output

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 Sample Output 1
4 3 5
2 3 1 2
2
1 3 3
2
1 1 1
2
3
-1
4
Sample Input 2 Sample Output 2
6 3 6
1 2 3 2 1 1
2
1 2 1
2
1 4 1
1 6 2
2
3
3
4