#include <bits/stdc++.h>
using namespace std;
template <typename T>
istream& operator>>(istream& is, vector<T>& v) {
  for (T& x : v) is >> x;
  return is;
}
template <typename T>
ostream& operator<<(ostream& os, const vector<T>& v) {
  for (size_t i = 0; i < v.size(); i++) {
    os << v[i] << (i + 1 == v.size() ? "" : " ");
  }
  return os;
}
template <typename T, typename U>
ostream& operator<<(ostream& os, const pair<T, U>& p) {
  os << '(' << p.first << ',' << p.second << ')';
  return os;
}
template <typename T, typename U>
ostream& operator<<(ostream& os, const map<T, U>& m) {
  os << '{';
  for (auto itr = m.begin(); itr != m.end();) {
    os << '(' << itr->first << ',' << itr->second << ')';
    if (++itr != m.end()) os << ',';
  }
  os << '}';
  return os;
}
template <typename T, typename U>
ostream& operator<<(ostream& os, const unordered_map<T, U>& m) {
  os << '{';
  for (auto itr = m.begin(); itr != m.end();) {
    os << '(' << itr->first << ',' << itr->second << ')';
    if (++itr != m.end()) os << ',';
  }
  os << '}';
  return os;
}
template <typename T>
ostream& operator<<(ostream& os, const set<T>& s) {
  os << '{';
  for (auto itr = s.begin(); itr != s.end();) {
    os << *itr;
    if (++itr != s.end()) os << ',';
  }
  os << '}';
  return os;
}
template <typename T>
ostream& operator<<(ostream& os, const multiset<T>& s) {
  os << '{';
  for (auto itr = s.begin(); itr != s.end();) {
    os << *itr;
    if (++itr != s.end()) os << ',';
  }
  os << '}';
  return os;
}
template <typename T>
ostream& operator<<(ostream& os, const unordered_set<T>& s) {
  os << '{';
  for (auto itr = s.begin(); itr != s.end();) {
    os << *itr;
    if (++itr != s.end()) os << ',';
  }
  os << '}';
  return os;
}
template <typename T>
ostream& operator<<(ostream& os, const deque<T>& v) {
  for (size_t i = 0; i < v.size(); i++) {
    os << v[i] << (i + 1 == v.size() ? "" : " ");
  }
  return os;
}
template <typename T, size_t N>
ostream& operator<<(ostream& os, const array<T, N>& v) {
  for (size_t i = 0; i < N; i++) {
    os << v[i] << (i + 1 == N ? "" : " ");
  }
  return os;
}
template <int i, typename T>
void print_tuple(ostream&, const T&) {}
template <int i, typename T, typename H, class... Args>
void print_tuple(ostream& os, const T& t) {
  if (i) os << ',';
  os << get<i>(t);
  print_tuple<i + 1, T, Args...>(os, t);
}
template <typename... Args>
ostream& operator<<(ostream& os, const tuple<Args...>& t) {
  os << '{';
  print_tuple<0, tuple<Args...>, Args...>(os, t);
  return os << '}';
}
void debug_out() { cerr << '\n'; }
template <class Head, class... Tail>
void debug_out(Head&& head, Tail&&... tail) {
  cerr << head;
  if (sizeof...(Tail) > 0) cerr << ", ";
  debug_out(move(tail)...);
}
template <typename T>
T gcd(T x, T y) {
  return y != 0 ? gcd(y, x % y) : x;
}
template <typename T>
T lcm(T x, T y) {
  return x / gcd(x, y) * y;
}
int topbit(signed t) { return t == 0 ? -1 : 31 - __builtin_clz(t); }
int topbit(long long t) { return t == 0 ? -1 : 63 - __builtin_clzll(t); }
int botbit(signed a) { return a == 0 ? 32 : __builtin_ctz(a); }
int botbit(long long a) { return a == 0 ? 64 : __builtin_ctzll(a); }
int popcount(signed t) { return __builtin_popcount(t); }
int popcount(long long t) { return __builtin_popcountll(t); }
bool ispow2(int i) { return i && (i & -i) == i; }
long long MSK(int n) { return (1LL << n) - 1; }
template <class T>
T ceil(T x, T y) {
  assert(y >= 1);
  return (x > 0 ? (x + y - 1) / y : x / y);
}
template <class T>
T floor(T x, T y) {
  assert(y >= 1);
  return (x > 0 ? x / y : (x - y + 1) / y);
}
template <class T1, class T2>
inline bool chmin(T1& a, T2 b) {
  if (a > b) {
    a = b;
    return true;
  }
  return false;
}
template <class T1, class T2>
inline bool chmax(T1& a, T2 b) {
  if (a < b) {
    a = b;
    return true;
  }
  return false;
}
template <typename T>
void mkuni(vector<T>& v) {
  sort(v.begin(), v.end());
  v.erase(unique(v.begin(), v.end()), v.end());
}
template <typename T>
int lwb(const vector<T>& v, const T& x) {
  return lower_bound(v.begin(), v.end(), x) - v.begin();
}
const int INF = 1e9;
const long long IINF = 1e18;
const int dx[4] = {1, 0, -1, 0}, dy[4] = {0, 1, 0, -1};
const char dir[4] = {'D', 'R', 'U', 'L'};
const long long MOD = 1000000007;
const int SQRT = 256;
int main() {
  cin.tie(0);
  ios::sync_with_stdio(false);
  int n, q;
  cin >> n >> q;
  vector<int> p(n);
  for (int& x : p) cin >> x, x--;
  vector<int> block(n), inv(n);
  for (int i = 0; i < n; i++) {
    inv[p[i]] = i;
    block[i] = i;
    for (int j = 0; j < SQRT; j++) block[i] = p[block[i]];
  }
  auto update = [&](int x, int y) {
    swap(inv[p[x]], inv[p[y]]);
    swap(p[x], p[y]);
    for (int _ = 0; _ < 2; swap(x, y), _++) {
      int to = x;
      for (int i = 0; i < SQRT; i++) to = p[to];
      for (int i = 0; i < SQRT; i++) {
        block[x] = to;
        x = inv[x];
        to = inv[to];
      }
    }
  };
  auto query = [&](int i, int k) {
    for (; k >= SQRT; k -= SQRT) i = block[i];
    for (; k > 0; k--) i = p[i];
    return i + 1;
  };
  for (; q--;) {
    int t;
    cin >> t;
    if (t == 1) {
      int x, y;
      cin >> x >> y;
      update(--x, --y);
    } else {
      int i, k;
      cin >> i >> k;
      cout << query(--i, k) << '\n';
    }
  }
  return 0;
}

### Prompt

Please provide a CPP coded solution to the problem described below:

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;
template <typename T>
istream& operator>>(istream& is, vector<T>& v) {
  for (T& x : v) is >> x;
  return is;
}
template <typename T>
ostream& operator<<(ostream& os, const vector<T>& v) {
  for (size_t i = 0; i < v.size(); i++) {
    os << v[i] << (i + 1 == v.size() ? "" : " ");
  }
  return os;
}
template <typename T, typename U>
ostream& operator<<(ostream& os, const pair<T, U>& p) {
  os << '(' << p.first << ',' << p.second << ')';
  return os;
}
template <typename T, typename U>
ostream& operator<<(ostream& os, const map<T, U>& m) {
  os << '{';
  for (auto itr = m.begin(); itr != m.end();) {
    os << '(' << itr->first << ',' << itr->second << ')';
    if (++itr != m.end()) os << ',';
  }
  os << '}';
  return os;
}
template <typename T, typename U>
ostream& operator<<(ostream& os, const unordered_map<T, U>& m) {
  os << '{';
  for (auto itr = m.begin(); itr != m.end();) {
    os << '(' << itr->first << ',' << itr->second << ')';
    if (++itr != m.end()) os << ',';
  }
  os << '}';
  return os;
}
template <typename T>
ostream& operator<<(ostream& os, const set<T>& s) {
  os << '{';
  for (auto itr = s.begin(); itr != s.end();) {
    os << *itr;
    if (++itr != s.end()) os << ',';
  }
  os << '}';
  return os;
}
template <typename T>
ostream& operator<<(ostream& os, const multiset<T>& s) {
  os << '{';
  for (auto itr = s.begin(); itr != s.end();) {
    os << *itr;
    if (++itr != s.end()) os << ',';
  }
  os << '}';
  return os;
}
template <typename T>
ostream& operator<<(ostream& os, const unordered_set<T>& s) {
  os << '{';
  for (auto itr = s.begin(); itr != s.end();) {
    os << *itr;
    if (++itr != s.end()) os << ',';
  }
  os << '}';
  return os;
}
template <typename T>
ostream& operator<<(ostream& os, const deque<T>& v) {
  for (size_t i = 0; i < v.size(); i++) {
    os << v[i] << (i + 1 == v.size() ? "" : " ");
  }
  return os;
}
template <typename T, size_t N>
ostream& operator<<(ostream& os, const array<T, N>& v) {
  for (size_t i = 0; i < N; i++) {
    os << v[i] << (i + 1 == N ? "" : " ");
  }
  return os;
}
template <int i, typename T>
void print_tuple(ostream&, const T&) {}
template <int i, typename T, typename H, class... Args>
void print_tuple(ostream& os, const T& t) {
  if (i) os << ',';
  os << get<i>(t);
  print_tuple<i + 1, T, Args...>(os, t);
}
template <typename... Args>
ostream& operator<<(ostream& os, const tuple<Args...>& t) {
  os << '{';
  print_tuple<0, tuple<Args...>, Args...>(os, t);
  return os << '}';
}
void debug_out() { cerr << '\n'; }
template <class Head, class... Tail>
void debug_out(Head&& head, Tail&&... tail) {
  cerr << head;
  if (sizeof...(Tail) > 0) cerr << ", ";
  debug_out(move(tail)...);
}
template <typename T>
T gcd(T x, T y) {
  return y != 0 ? gcd(y, x % y) : x;
}
template <typename T>
T lcm(T x, T y) {
  return x / gcd(x, y) * y;
}
int topbit(signed t) { return t == 0 ? -1 : 31 - __builtin_clz(t); }
int topbit(long long t) { return t == 0 ? -1 : 63 - __builtin_clzll(t); }
int botbit(signed a) { return a == 0 ? 32 : __builtin_ctz(a); }
int botbit(long long a) { return a == 0 ? 64 : __builtin_ctzll(a); }
int popcount(signed t) { return __builtin_popcount(t); }
int popcount(long long t) { return __builtin_popcountll(t); }
bool ispow2(int i) { return i && (i & -i) == i; }
long long MSK(int n) { return (1LL << n) - 1; }
template <class T>
T ceil(T x, T y) {
  assert(y >= 1);
  return (x > 0 ? (x + y - 1) / y : x / y);
}
template <class T>
T floor(T x, T y) {
  assert(y >= 1);
  return (x > 0 ? x / y : (x - y + 1) / y);
}
template <class T1, class T2>
inline bool chmin(T1& a, T2 b) {
  if (a > b) {
    a = b;
    return true;
  }
  return false;
}
template <class T1, class T2>
inline bool chmax(T1& a, T2 b) {
  if (a < b) {
    a = b;
    return true;
  }
  return false;
}
template <typename T>
void mkuni(vector<T>& v) {
  sort(v.begin(), v.end());
  v.erase(unique(v.begin(), v.end()), v.end());
}
template <typename T>
int lwb(const vector<T>& v, const T& x) {
  return lower_bound(v.begin(), v.end(), x) - v.begin();
}
const int INF = 1e9;
const long long IINF = 1e18;
const int dx[4] = {1, 0, -1, 0}, dy[4] = {0, 1, 0, -1};
const char dir[4] = {'D', 'R', 'U', 'L'};
const long long MOD = 1000000007;
const int SQRT = 256;
int main() {
  cin.tie(0);
  ios::sync_with_stdio(false);
  int n, q;
  cin >> n >> q;
  vector<int> p(n);
  for (int& x : p) cin >> x, x--;
  vector<int> block(n), inv(n);
  for (int i = 0; i < n; i++) {
    inv[p[i]] = i;
    block[i] = i;
    for (int j = 0; j < SQRT; j++) block[i] = p[block[i]];
  }
  auto update = [&](int x, int y) {
    swap(inv[p[x]], inv[p[y]]);
    swap(p[x], p[y]);
    for (int _ = 0; _ < 2; swap(x, y), _++) {
      int to = x;
      for (int i = 0; i < SQRT; i++) to = p[to];
      for (int i = 0; i < SQRT; i++) {
        block[x] = to;
        x = inv[x];
        to = inv[to];
      }
    }
  };
  auto query = [&](int i, int k) {
    for (; k >= SQRT; k -= SQRT) i = block[i];
    for (; k > 0; k--) i = p[i];
    return i + 1;
  };
  for (; q--;) {
    int t;
    cin >> t;
    if (t == 1) {
      int x, y;
      cin >> x >> y;
      update(--x, --y);
    } else {
      int i, k;
      cin >> i >> k;
      cout << query(--i, k) << '\n';
    }
  }
  return 0;
}

```