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>
  std::mt19937_64 gen(
      std::chrono::steady_clock::now().time_since_epoch().count());
  std::mt19937 gen1(std::chrono::steady_clock::now().time_since_epoch().count());
  int rng(int l, int r) { return std::uniform_int_distribution<int>(l, r)(gen); }
  const long double PI = atan(1.0) * 4;
  const int32_t INF32 = 2e9 + 7;
  const int64_t INF64 = 3e18;
  const int32_t LOG = 21;
  int32_t MOD = 1e9 + 7;
  using namespace std;
  void my_debugger(string second, int LINE_NUM) { cerr << '\n'; }
  template <typename start, typename... end>
  void my_debugger(string second, int LINE_NUM, start x, end... y) {
    if (second.back() != ',') {
      second += ',';
      cerr << "LINE(" << LINE_NUM << "): ";
    }
    int i = second.find(',');
    cerr << second.substr(0, i) << " = " << x;
    second = second.substr(i + 1);
    if (!second.empty()) cerr << ", ";
    my_debugger(second, LINE_NUM, y...);
  }
  void setMod(int mod_val) { MOD = mod_val; }
  void files_init() {
    freopen("file.in", "r", stdin);
    freopen("file.out", "w", stdout);
  }
  const int N = 1e6 + 5;
  const int LOGN = 20;
  int32_t main() {
    ios_base::sync_with_stdio(false), cin.tie(nullptr);
    int tests = 1;
    for (int ii = 0; ii < (int)tests; ii++) {
      int n, q;
      cin >> n >> q;
      int BLOCK = sqrt(n + 0.5);
      vector<int> a(n + 1);
      for (int i = 1; i < (int)n + 1; i++) cin >> a[i];
      vector<int> nxt(n + 1), prev(n + 1), nxtBlock(n + 1);
      for (int i = 1; i < (int)n + 1; i++) {
        nxt[i] = a[i];
        prev[a[i]] = i;
      }
      for (int i = 1; i < (int)n + 1; i++) {
        int cur = i;
        for (int j = 0; j < (int)BLOCK; j++) cur = nxt[cur];
        nxtBlock[i] = cur;
      }
      for (int query = 0; query < (int)q; query++) {
        int type;
        cin >> type;
        if (type == 1) {
          int x, y;
          cin >> x >> y;
          nxt[x] = a[y];
          nxt[y] = a[x];
          prev[a[y]] = x;
          prev[a[x]] = y;
          int temp1 = a[x], temp2 = a[y];
          a[x] = temp2, a[y] = temp1;
          {
            vector<int> vals;
            int cur = x;
            for (int i = 0; i < (int)BLOCK; i++) {
              cur = nxt[cur];
              vals.push_back(cur);
            }
            cur = x;
            int ptr = vals.size() - 1;
            for (int i = 0; i < (int)BLOCK; i++) {
              nxtBlock[cur] = vals[ptr];
              ptr--;
              cur = prev[cur];
            }
          }
          {
            vector<int> vals;
            int cur = y;
            for (int i = 0; i < (int)BLOCK; i++) {
              cur = nxt[cur];
              vals.push_back(cur);
            }
            cur = y;
            int ptr = vals.size() - 1;
            for (int i = 0; i < (int)BLOCK; i++) {
              nxtBlock[cur] = vals[ptr];
              ptr--;
              cur = prev[cur];
            }
          }
        } else {
          int i, k;
          cin >> i >> k;
          int blocks = k / BLOCK;
          int rem = k % BLOCK;
          int cur = i;
          for (int i = 0; i < (int)blocks; i++) cur = nxtBlock[cur];
          for (int i = 0; i < (int)rem; i++) cur = nxt[cur];
          cout << cur << '\n';
        }
      }
    }
    return 0;
  }
  