#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using ull = unsigned long long;
using ld = long double;
template <typename T1, typename T2>
inline void chkmin(T1& x, const T2& y) {
  if (y < x) x = y;
}
template <typename T1, typename T2>
inline void chkmax(T1& x, const T2& y) {
  if (x < y) x = y;
}
const int N = 1e5 + 10;
const int B = 250;
struct Node {
  int next_node;
  int prev_node;
  int jump;
};
int n, q;
Node nodes[N];
bool used[N];
int find_jump(int v) {
  for (int i = 0; i < B; ++i) {
    v = nodes[v].next_node;
  }
  return v;
}
void build() {
  for (int i = 0; i < n; ++i) {
    if (used[i]) continue;
    int v = i;
    int jump = find_jump(i);
    while (!used[v]) {
      used[v] = true;
      nodes[v].jump = jump;
      v = nodes[v].next_node;
      jump = nodes[jump].next_node;
    }
  }
}
void relax_jumps(int v) {
  int jump = v;
  for (int i = 0; i < B; ++i) {
    v = nodes[v].prev_node;
  }
  for (int i = 0; i <= B; ++i) {
    nodes[v].jump = jump;
    v = nodes[v].next_node;
    jump = nodes[jump].next_node;
  }
}
void upd(int i, int j) {
  int next_i = nodes[i].next_node;
  int next_j = nodes[j].next_node;
  nodes[i].next_node = next_j;
  nodes[j].next_node = next_i;
  nodes[next_i].prev_node = j;
  nodes[next_j].prev_node = i;
  relax_jumps(i);
  relax_jumps(j);
}
int getAns(int v, int k) {
  while (k) {
    if (k >= B) {
      v = nodes[v].jump;
      k -= B;
    } else {
      v = nodes[v].next_node;
      --k;
    }
  }
  return v;
}
signed main() {
  ios_base::sync_with_stdio(0), cin.tie(0), cout.tie(0);
  cout.precision(20), cout.setf(ios::fixed);
  cin >> n >> q;
  for (int i = 0; i < n; ++i) {
    cin >> nodes[i].next_node;
    --nodes[i].next_node;
    nodes[nodes[i].next_node].prev_node = i;
  }
  build();
  while (q--) {
    int t;
    cin >> t;
    if (t == 1) {
      int i, j;
      cin >> i >> j;
      --i;
      --j;
      upd(i, j);
    } else if (t == 2) {
      int v, k;
      cin >> v >> k;
      --v;
      cout << getAns(v, k) + 1 << '\n';
    } else {
      assert(false);
    }
  }
  return 0;
}

### Prompt

Create a solution in Cpp for the following problem:

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.

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using ull = unsigned long long;
using ld = long double;
template <typename T1, typename T2>
inline void chkmin(T1& x, const T2& y) {
  if (y < x) x = y;
}
template <typename T1, typename T2>
inline void chkmax(T1& x, const T2& y) {
  if (x < y) x = y;
}
const int N = 1e5 + 10;
const int B = 250;
struct Node {
  int next_node;
  int prev_node;
  int jump;
};
int n, q;
Node nodes[N];
bool used[N];
int find_jump(int v) {
  for (int i = 0; i < B; ++i) {
    v = nodes[v].next_node;
  }
  return v;
}
void build() {
  for (int i = 0; i < n; ++i) {
    if (used[i]) continue;
    int v = i;
    int jump = find_jump(i);
    while (!used[v]) {
      used[v] = true;
      nodes[v].jump = jump;
      v = nodes[v].next_node;
      jump = nodes[jump].next_node;
    }
  }
}
void relax_jumps(int v) {
  int jump = v;
  for (int i = 0; i < B; ++i) {
    v = nodes[v].prev_node;
  }
  for (int i = 0; i <= B; ++i) {
    nodes[v].jump = jump;
    v = nodes[v].next_node;
    jump = nodes[jump].next_node;
  }
}
void upd(int i, int j) {
  int next_i = nodes[i].next_node;
  int next_j = nodes[j].next_node;
  nodes[i].next_node = next_j;
  nodes[j].next_node = next_i;
  nodes[next_i].prev_node = j;
  nodes[next_j].prev_node = i;
  relax_jumps(i);
  relax_jumps(j);
}
int getAns(int v, int k) {
  while (k) {
    if (k >= B) {
      v = nodes[v].jump;
      k -= B;
    } else {
      v = nodes[v].next_node;
      --k;
    }
  }
  return v;
}
signed main() {
  ios_base::sync_with_stdio(0), cin.tie(0), cout.tie(0);
  cout.precision(20), cout.setf(ios::fixed);
  cin >> n >> q;
  for (int i = 0; i < n; ++i) {
    cin >> nodes[i].next_node;
    --nodes[i].next_node;
    nodes[nodes[i].next_node].prev_node = i;
  }
  build();
  while (q--) {
    int t;
    cin >> t;
    if (t == 1) {
      int i, j;
      cin >> i >> j;
      --i;
      --j;
      upd(i, j);
    } else if (t == 2) {
      int v, k;
      cin >> v >> k;
      --v;
      cout << getAns(v, k) + 1 << '\n';
    } else {
      assert(false);
    }
  }
  return 0;
}

```