Problem: 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 ci be the number of occurrences of i in al: r, where al: r is the subarray of a from l-th element to r-th inclusive. Find the Mex of {c0, c1, ..., c109}
  2. You are given two integers p to x. Change ap 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 c0 = 0 and 0 is never the answer for the query of the second type.

Input

The first line of input contains two integers n and q (1 ≤ n, q ≤ 100 000) — the length of the array and the number of queries respectively.

The second line of input contains n integers — a1, a2, ..., an (1 ≤ ai ≤ 109).

Each of the next q lines describes a single query.

The first type of query is described by three integers ti = 1, li, ri, where 1 ≤ li ≤ ri ≤ n — the bounds of the subarray.

The second type of query is described by three integers ti = 2, pi, xi, where 1 ≤ pi ≤ n is the index of the element, which must be changed and 1 ≤ xi ≤ 109 is the new value.

Output

For each query of the first type output a single integer — the Mex of {c0, c1, ..., c109}.

Example

Input

10 4
1 2 3 1 1 2 2 2 9 9
1 1 1
1 2 8
2 7 1
1 2 8


Output

2
3
2

Note

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

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

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

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
const int maxn = 2e5 + 7;
const int inf = INT_MAX;
const long long inff = 1e18;
const long long mod = 1e9 + 7;
int B;
int n, q;
int a[maxn], tmpa[maxn];
int type[maxn], X[maxn], Y[maxn], ans[maxn];
int appear[maxn], cnt[maxn];
struct Event {
  int place, orivalue, newvalue, times;
  Event(int _p, int _o, int _n, int _t)
      : place(_p), orivalue(_o), newvalue(_n), times(_t) {}
};
struct Query {
  int l, r, id;
  Query(int _l, int _r, int _id) : l(_l), r(_r), id(_id) {}
  bool operator<(const Query &rhs) const {
    if (l / B != rhs.l / B)
      return l < rhs.l;
    else if (r / B != rhs.r / B)
      return r < rhs.r;
    else
      return id < rhs.id;
  }
};
vector<Event> v1;
vector<Query> v2;
vector<int> values;
void Add(int x) {
  cnt[appear[a[x]]]--;
  cnt[appear[a[x]] + 1]++;
  appear[a[x]]++;
}
void Sub(int x) {
  cnt[appear[a[x]]]--;
  cnt[appear[a[x]] - 1]++;
  appear[a[x]]--;
}
int32_t main() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  cin >> n >> q;
  B = int(pow(n, 2.0 / 3.0));
  for (int i = 1; i <= n; i++) {
    cin >> a[i];
    tmpa[i] = a[i];
    values.push_back(a[i]);
  }
  for (int i = 1; i <= q; i++) {
    cin >> type[i] >> X[i] >> Y[i];
    values.push_back(Y[i]);
    if (type[i] == 1)
      v2.push_back(Query(X[i], Y[i], i));
    else {
      v1.push_back(Event(X[i], tmpa[X[i]], Y[i], i));
      tmpa[X[i]] = Y[i];
    }
  }
  sort((values).begin(), (values).end());
  values.resize(unique((values).begin(), (values).end()) - values.begin());
  for (Event &i : v1)
    i.orivalue = lower_bound((values).begin(), (values).end(), i.orivalue) -
                 values.begin() + 1,
    i.newvalue = lower_bound((values).begin(), (values).end(), i.newvalue) -
                 values.begin() + 1;
  for (int i = 1; i <= n; i++)
    a[i] = lower_bound((values).begin(), (values).end(), a[i]) -
           values.begin() + 1;
  sort((v2).begin(), (v2).end());
  cnt[0] = 1e8;
  int L = 1, R = 0, att = -1;
  for (Query i : v2) {
    while (att + 1 < (int)((v1).size()) && v1[att + 1].times <= i.id) {
      if (v1[att + 1].place >= L && v1[att + 1].place <= R)
        Sub(v1[att + 1].place);
      a[v1[att + 1].place] = v1[att + 1].newvalue;
      if (v1[att + 1].place >= L && v1[att + 1].place <= R)
        Add(v1[att + 1].place);
      att++;
    }
    while (att >= 0 && v1[att].times > i.id) {
      if (v1[att].place >= L && v1[att].place <= R) Sub(v1[att].place);
      a[v1[att].place] = v1[att].orivalue;
      if (v1[att].place >= L && v1[att].place <= R) Add(v1[att].place);
      att--;
    }
    while (R < i.r) Add(++R);
    while (L > i.l) Add(--L);
    while (R > i.r) Sub(R--);
    while (L < i.l) Sub(L++);
    for (int j = 1;; j++)
      if (cnt[j] == 0) {
        ans[i.id] = j;
        break;
      }
  }
  for (int i = 1; i <= q; i++)
    if (type[i] == 1) cout << ans[i] << '\n';
}