CF940F.Machine Learning

You come home and fell some unpleasant smell. Where is it coming from?

You are given an array $a$ . You have to answer the following queries:

1. You are given two integers $l$ and $r$ . Let $c_{i}$ be the number of occurrences of $i$ in $a_{l:r}$ , where $a_{l:r}$ is the subarray of $a$ from $l$ -th element to $r$ -th inclusive. Find the Mex of ${c_{0},c_{1},...,c_{10^{9}}}$
2. You are given two integers $p$ to $x$ . Change $a_{p}$ to $x$ .

The Mex of a multiset of numbers is the smallest non-negative integer not in the set.

Note that in this problem all elements of $a$ are positive, which means that $c_{0}$ = 0 and $0$ is never the answer for the query of the second type.

The first line of input contains two integers $n$ and $q$ ( $1<=n,q<=100000$ ) — the length of the array and the number of queries respectively.

The second line of input contains $n$ integers — $a_{1}$ , $a_{2}$ , $...$ , $a_{n}$ ( $1<=a_{i}<=10^{9}$ ).

Each of the next $q$ lines describes a single query.

The first type of query is described by three integers $t_{i}=1$ , $l_{i}$ , $r_{i}$ , where $1<=l_{i}<=r_{i}<=n$ — the bounds of the subarray.

The second type of query is described by three integers $t_{i}=2$ , $p_{i}$ , $x_{i}$ , where $1<=p_{i}<=n$ is the index of the element, which must be changed and $1<=x_{i}<=10^{9}$ is the new value.

For each query of the first type output a single integer — the Mex of ${c_{0},c_{1},...,c_{10^{9}}}$ .

The subarray of the first query consists of the single element — $1$ .

The subarray of the second query consists of four $2$ s, one $3$ and two $1$ s.

The subarray of the fourth query consists of three $1$ s, three $2$ s and one $3$ .