description: You are given a permutation p of n elements. A permutation of n elements is an array of length n containing each integer from 1 to n exactly once. For example, [1, 2, 3] and [4, 3, 5, 1, 2] are permutations, but [1, 2, 4] and [4, 3, 2, 1, 2] are not permutations. You should perform q queries.
  
  There are two types of queries:
  
    * 1 x y — swap p_x and p_y. 
    * 2 i k — print the number that i will become if we assign i = p_i k times. 
  
  Input
  
  The first line contains two integers n and q (1 ≤ n, q ≤ 10^5).
  
  The second line contains n integers p_1, p_2, ..., p_n.
  
  Each of the next q lines contains three integers. The first integer is t (1 ≤ t ≤ 2) — type of query. If t = 1, then the next two integers are x and y (1 ≤ x, y ≤ n; x ≠ y) — first-type query. If t = 2, then the next two integers are i and k (1 ≤ i, k ≤ n) — second-type query.
  
  It is guaranteed that there is at least one second-type query.
  
  Output
  
  For every second-type query, print one integer in a new line — answer to this query.
  
  Examples
  
  Input
  
  
  5 4
  5 3 4 2 1
  2 3 1
  2 1 2
  1 1 3
  2 1 2
  
  
  Output
  
  
  4
  1
  2
  
  
  Input
  
  
  5 9
  2 3 5 1 4
  2 3 5
  2 5 5
  2 5 1
  2 5 3
  2 5 4
  1 5 4
  2 5 3
  2 2 5
  2 5 1
  
  
  Output
  
  
  3
  5
  4
  2
  3
  3
  3
  1
  
  Note
  
  In the first example p = \{5, 3, 4, 2, 1\}. 
  
  The first query is to print p_3. The answer is 4.
  
  The second query is to print p_{p_1}. The answer is 1.
  
  The third query is to swap p_1 and p_3. Now p = \{4, 3, 5, 2, 1\}.
  
  The fourth query is to print p_{p_1}. The answer is 2.
solution: #include <bits/stdc++.h>
  using namespace std;
  void solve();
  int main() {
    ios::sync_with_stdio(0);
    cin.tie(0);
    cout.tie(0);
    solve();
  }
  const long long N = 1e5 + 100, INF = 2e18, MOD = 1e9 + 7;
  mt19937_64 rnd(time(0));
  struct node {
    node* l = nullptr;
    node* r = nullptr;
    node* p = nullptr;
    long long x, y, sz;
    node(long long x) : x(x), y(rnd()), sz(1) {}
  };
  long long size(node* t) {
    if (t == nullptr) return 0;
    return t->sz;
  }
  void update(node* t) { t->sz = size(t->l) + size(t->r) + 1; }
  pair<node*, node*> split(node* t, long long k) {
    if (t == nullptr) return {nullptr, nullptr};
    if (k >= size(t->l) + 1) {
      pair<node*, node*> z = split(t->r, k - size(t->l) - 1);
      if (z.first != nullptr) z.first->p = t;
      if (z.second != nullptr) z.second->p = nullptr;
      t->r = z.first;
      update(t);
      return {t, z.second};
    } else {
      pair<node*, node*> z = split(t->l, k);
      if (z.first != nullptr) z.first->p = nullptr;
      if (z.second != nullptr) z.second->p = t;
      t->l = z.second;
      update(t);
      return {z.first, t};
    }
  }
  node* merge(node* a, node* b) {
    if (a == nullptr) return b;
    if (b == nullptr) return a;
    if (a->y > b->y) {
      a->r = merge(a->r, b);
      if (a->r != nullptr) a->r->p = a;
      update(a);
      return a;
    } else {
      b->l = merge(a, b->l);
      if (b->l != nullptr) b->l->p = b;
      update(b);
      return b;
    }
  }
  pair<node*, long long> find(node* t) {
    long long pos = size(t->l);
    while (t->p != nullptr) {
      node* z = t;
      t = t->p;
      if (t->r == z) {
        pos += size(t->l) + 1;
      }
    }
    return {t, pos};
  }
  void pri(node* t) {
    if (t->l != nullptr) pri(t->l);
    cout << t->x + 1 << " ";
    if (t->r != nullptr) pri(t->r);
  }
  void print(node* t) {
    pri(find(t).first);
    cout << endl;
  }
  long long n, q, p[N];
  vector<long long> go;
  node* t[N];
  bool used[N];
  void dfs(long long v) {
    used[v] = true;
    go.push_back(v);
    if (!used[p[v]]) dfs(p[v]);
  }
  void solve() {
    cin >> n >> q;
    for (long long i = 0; i < n; i++) {
      cin >> p[i];
      p[i]--;
      t[i] = new node(i);
    }
    for (long long i = 0; i < n; i++) {
      if (!used[i]) {
        go.clear();
        dfs(i);
        node* z = t[go[0]];
        for (long long j = 1; j < go.size(); j++) {
          z = merge(z, t[go[j]]);
        }
      }
    }
    for (long long qq = 0; qq < q; qq++) {
      long long ty, x, y;
      cin >> ty >> x >> y;
      if (ty == 1) {
        x--, y--;
        pair<node*, long long> z1 = find(t[x]);
        pair<node*, long long> z2 = find(t[y]);
        if (z1.first == z2.first) {
          if (z1.second > z2.second) swap(z1, z2);
          pair<node*, node*> sp1 = split(z1.first, z2.second + 1);
          pair<node*, node*> sp2 = split(sp1.first, z1.second + 1);
          merge(sp2.first, sp1.second);
        } else {
          pair<node*, node*> sp1 = split(z1.first, z1.second + 1);
          pair<node*, node*> sp2 = split(z2.first, z2.second + 1);
          node* tt = merge(sp2.second, sp2.first);
          merge(merge(sp1.first, tt), sp1.second);
        }
      } else {
        x--;
        pair<node*, long long> z = find(t[x]);
        long long len = size(z.first);
        y %= len;
        node* tt = z.first;
        if (z.second + y < len) {
          y = z.second + y;
        } else {
          y = z.second + y - len;
        }
        pair<node*, node*> e = split(tt, y + 1);
        pair<node*, node*> u = split(e.first, y);
        cout << u.second->x + 1 << '\n';
        merge(merge(u.first, u.second), e.second);
      }
    }
  }
  