#include <bits/stdc++.h>
#pragma GCC optimize("O3")
using namespace std;
template <class T>
using pq = priority_queue<T>;
template <class T>
using pqg = priority_queue<T, vector<T>, greater<T>>;
int scan() { return getchar(); }
template <class T>
void scan(T a) {
  cin >> a;
}
void scan(int &a) { cin >> a; }
void scan(long long &a) { cin >> a; }
void scan(char &a) { cin >> a; }
void scan(double &a) { cin >> a; }
void scan(long double &a) { cin >> a; }
void scan(char a[]) { scanf("%s", a); }
void scan(string &a) { cin >> a; }
template <class T>
void scan(vector<T> &);
template <class T, size_t size>
void scan(array<T, size> &);
template <class T, class L>
void scan(pair<T, L> &);
template <class T, size_t size>
void scan(T (&)[size]);
template <class T>
void scan(vector<T> &a) {
  for (auto &i : a) scan(i);
}
template <class T>
void scan(deque<T> &a) {
  for (auto &i : a) scan(i);
}
template <class T, size_t size>
void scan(array<T, size> &a) {
  for (auto &i : a) scan(i);
}
template <class T, class L>
void scan(pair<T, L> &p) {
  scan(p.first);
  scan(p.second);
}
template <class T, size_t size>
void scan(T (&a)[size]) {
  for (auto &i : a) scan(i);
}
template <class T>
void scan(T &a) {
  cin >> a;
}
void IN() {}
template <class Head, class... Tail>
void IN(Head &head, Tail &...tail) {
  scan(head);
  IN(tail...);
}
string stin() {
  string s;
  cin >> s;
  return s;
}
template <class T, class S>
inline bool chmax(T &a, S b) {
  if (a < b) {
    a = b;
    return 1;
  }
  return 0;
}
template <class T, class S>
inline bool chmin(T &a, S b) {
  if (a > b) {
    a = b;
    return 1;
  }
  return 0;
}
vector<int> iota(int n) {
  vector<int> a(n);
  iota(begin(a), end(a), 0);
  return a;
}
template <class T>
void UNIQUE(vector<T> &x) {
  sort(begin(x), end(x));
  x.erase(unique(begin(x), end(x)), x.end());
}
int in() {
  int x;
  cin >> x;
  return x;
}
long long lin() {
  unsigned long long x;
  cin >> x;
  return x;
}
void print() { putchar(' '); }
void print(bool a) { cout << a; }
void print(int a) { cout << a; }
void print(long long a) { cout << a; }
void print(char a) { cout << a; }
void print(string &a) { cout << a; }
void print(double a) { cout << a; }
template <class T>
void print(const vector<T> &);
template <class T, size_t size>
void print(const array<T, size> &);
template <class T, class L>
void print(const pair<T, L> &p);
template <class T, size_t size>
void print(const T (&)[size]);
template <class T>
void print(const vector<T> &a) {
  if (a.empty()) return;
  print(a[0]);
  for (auto i = a.begin(); ++i != a.end();) {
    cout << " ";
    print(*i);
  }
  cout << endl;
}
template <class T>
void print(const deque<T> &a) {
  if (a.empty()) return;
  print(a[0]);
  for (auto i = a.begin(); ++i != a.end();) {
    cout << " ";
    print(*i);
  }
}
template <class T, size_t size>
void print(const array<T, size> &a) {
  print(a[0]);
  for (auto i = a.begin(); ++i != a.end();) {
    cout << " ";
    print(*i);
  }
}
template <class T, class L>
void print(const pair<T, L> &p) {
  cout << '(';
  print(p.first);
  cout << ",";
  print(p.second);
  cout << ')';
}
template <class T>
void print(set<T> &x) {
  for (auto e : x) print(e), cout << " ";
  cout << endl;
}
template <class T>
void print(multiset<T> &x) {
  for (auto e : x) print(e), cout << " ";
  cout << endl;
}
template <class T, size_t size>
void print(const T (&a)[size]) {
  print(a[0]);
  for (auto i = a; ++i != end(a);) {
    cout << " ";
    print(*i);
  }
}
template <class T>
void print(const T &a) {
  cout << a;
}
int out() {
  putchar('\n');
  return 0;
}
template <class T>
int out(const T &t) {
  print(t);
  putchar('\n');
  return 0;
}
template <class Head, class... Tail>
int out(const Head &head, const Tail &...tail) {
  print(head);
  putchar(' ');
  out(tail...);
  return 0;
}
long long gcd(long long a, long long b) {
  while (b) {
    long long c = b;
    b = a % b;
    a = c;
  }
  return a;
}
long long lcm(long long a, long long b) {
  if (!a || !b) return 0;
  return a * b / gcd(a, b);
}
vector<pair<long long, long long>> factor(long long x) {
  vector<pair<long long, long long>> ans;
  for (long long i = 2; i * i <= x; i++)
    if (x % i == 0) {
      ans.push_back({i, 1});
      while ((x /= i) % i == 0) ans.back().second++;
    }
  if (x != 1) ans.push_back({x, 1});
  return ans;
}
vector<int> divisor(int x) {
  vector<int> ans;
  for (int i = 1; i * i <= x; i++)
    if (x % i == 0) {
      ans.push_back(i);
      if (i * i != x) ans.push_back(x / i);
    }
  return ans;
}
template <typename T>
void zip(vector<T> &x) {
  vector<T> y = x;
  sort(begin(y), end(y));
  for (int i = 0; i < x.size(); ++i) {
    x[i] = distance((y).begin(), lower_bound(begin(y), end(y), (x[i])));
  }
}
int popcount(long long x) { return __builtin_popcountll(x); }
mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
int rnd(int n) { return uniform_int_distribution<int>(0, n - 1)(rng); }
template <typename T>
void shuffle(vector<T> &v) {
  for (long long i = v.size() - 1; i >= 1; --i) {
    swap(v[i], v[rnd(i)]);
  }
}
vector<string> YES{"NO", "YES"};
vector<string> Yes{"No", "Yes"};
vector<string> yes{"no", "yes"};
template <class... T>
void err(const T &...) {}
template <typename T>
struct edge {
  int from, to;
  T cost;
  int id;
  edge(int to, T cost) : from(-1), to(to), cost(cost) {}
  edge(int from, int to, T cost) : from(from), to(to), cost(cost) {}
  edge &operator=(const int &x) {
    to = x;
    return *this;
  }
  operator int() const { return to; }
};
template <typename T>
using Edges = vector<edge<T>>;
template <typename T>
using WeightedTree = vector<Edges<T>>;
template <typename T>
using Edges = vector<edge<T>>;
template <typename T>
using WeightedGraph = vector<Edges<T>>;
template <typename T>
using Matrix = vector<vector<T>>;
using Graph = vector<vector<int>>;
using tree = vector<vector<int>>;
tree getTree(int n, int offset = 1) {
  tree res(n);
  for (int i = 0; i < n - 1; i++) {
    int a, b;
    cin >> a >> b;
    a -= offset, b -= offset;
    res[a].emplace_back(b);
    res[b].emplace_back(a);
  }
  return res;
}
template <typename T>
WeightedTree<T> getWeightedTree(int n, int offset = 1) {
  WeightedTree<T> res(n);
  for (int i = 0; i < n - 1; i++) {
    int a, b;
    cin >> a >> b;
    a -= offset, b -= offset;
    T c;
    cin >> c;
    res[a].emplace_back(b, c);
    res[b].emplace_back(a, c);
  }
  return res;
}
Graph getGraph(int n, int m, int offset = 1) {
  Graph res(n);
  for (int i = 0; i < m; ++i) {
    int a, b;
    cin >> a >> b;
    a -= offset, b -= offset;
    res[a].emplace_back(b);
    res[b].emplace_back(a);
  }
  return res;
}
template <typename T>
WeightedGraph<T> getWeightedGraph(int n, int m, int offset = 1) {
  WeightedGraph<T> res(n);
  for (int i = 0; i < m; ++i) {
    int a, b;
    cin >> a >> b;
    T c;
    cin >> c;
    res[a].emplace_back(b, c);
    res[b].emplace_back(a, c);
  }
}
struct Setup_io {
  Setup_io() {
    ios_base::sync_with_stdio(0), cin.tie(0), cout.tie(0);
    cout << fixed << setprecision(15);
  }
} setup_io;
template <typename T>
vector<T> dijkstra(WeightedGraph<T> &g, int s) {
  const auto INF = numeric_limits<T>::max();
  vector<T> d(g.size(), INF);
  using P = pair<T, int>;
  priority_queue<P, vector<P>, greater<P>> pq;
  d[s] = 0;
  pq.emplace(0, s);
  while (!pq.empty()) {
    auto [cost, now] = pq.top();
    pq.pop();
    if (d[now] < cost) continue;
    for (auto &e : g[now]) {
      if (d[e] <= d[now] + e.cost) continue;
      d[e] = d[now] + e.cost;
      pq.emplace(d[e], e.to);
    }
  }
  return d;
}
int main() {
  int n, q, s;
  IN(n, q, s);
  int N = 1;
  while (N < n) {
    N <<= 1;
  }
  WeightedGraph<long long> g(N * 4 + n);
  while (q--) {
    int id;
    IN(id);
    if (id == 1) {
      int v, u, w;
      IN(v, u, w);
      g[v - 1].emplace_back(u - 1, w);
    }
    if (id == 2) {
      int v, l, r, w;
      IN(v, l, r, w);
      l--;
      for (int d = r - l; d >= 1; d = r - l) {
        int L = l | ((1U << 31) >> __builtin_clz(d));
        int k = __builtin_ctz(L);
        g[v - 1].emplace_back(((N | l) >> k) + n, w);
        l += L & (-L);
      }
    }
    if (id == 3) {
      int v, l, r, w;
      IN(v, l, r, w);
      l--;
      for (int d = r - l; d >= 1; d = r - l) {
        int L = l | ((1U << 31) >> __builtin_clz(d));
        int k = __builtin_ctz(L);
        g[((N | l) >> k) + n + N * 2].emplace_back(v - 1, w);
        l += L & (-L);
      }
    }
  }
  for (long long i = 0; i < N - 1; ++i) {
    g[n + i].emplace_back(n + i * 2, 0);
    g[n + i].emplace_back(n + i * 2 + 1, 0);
  }
  for (long long i = 0; i < N - 1; ++i) {
    g[n + N * 2 + i * 2].emplace_back(n + N * 2 + i, 0);
    g[n + N * 2 + i * 2 + 1].emplace_back(n + N * 2 + i, 0);
  }
  for (long long i = 0; i < n; ++i) {
    g[n + N + i].emplace_back(i, 0);
    g[i].emplace_back(n + N * 3 + i, 0);
  }
  auto d = dijkstra(g, s - 1);
  for (long long i = 0; i < n; ++i) {
    if (d[i] == LLONG_MAX)
      cout << -1;
    else
      cout << d[i];
    cout << " ";
  }
  cout << '\n';
}

### Prompt

Generate a Cpp solution to the following problem:

Rick and his co-workers have made a new radioactive formula and a lot of bad guys are after them. So Rick wants to give his legacy to Morty before bad guys catch them. 

There are n planets in their universe numbered from 1 to n. Rick is in planet number s (the earth) and he doesn't know where Morty is. As we all know, Rick owns a portal gun. With this gun he can open one-way portal from a planet he is in to any other planet (including that planet). But there are limits on this gun because he's still using its free trial.

<image>

By default he can not open any portal by this gun. There are q plans in the website that sells these guns. Every time you purchase a plan you can only use it once but you can purchase it again if you want to use it more.

Plans on the website have three types:

  1. With a plan of this type you can open a portal from planet v to planet u. 
  2. With a plan of this type you can open a portal from planet v to any planet with index in range [l, r]. 
  3. With a plan of this type you can open a portal from any planet with index in range [l, r] to planet v. 



Rick doesn't known where Morty is, but Unity is going to inform him and he wants to be prepared for when he finds and start his journey immediately. So for each planet (including earth itself) he wants to know the minimum amount of money he needs to get from earth to that planet.

Input

The first line of input contains three integers n, q and s (1 ≤ n, q ≤ 105, 1 ≤ s ≤ n) — number of planets, number of plans and index of earth respectively.

The next q lines contain the plans. Each line starts with a number t, type of that plan (1 ≤ t ≤ 3). If t = 1 then it is followed by three integers v, u and w where w is the cost of that plan (1 ≤ v, u ≤ n, 1 ≤ w ≤ 109). Otherwise it is followed by four integers v, l, r and w where w is the cost of that plan (1 ≤ v ≤ n, 1 ≤ l ≤ r ≤ n, 1 ≤ w ≤ 109).

Output

In the first and only line of output print n integers separated by spaces. i-th of them should be minimum money to get from earth to i-th planet, or  - 1 if it's impossible to get to that planet.

Examples

Input

3 5 1
2 3 2 3 17
2 3 2 2 16
2 2 2 3 3
3 3 1 1 12
1 3 3 17


Output

0 28 12 


Input

4 3 1
3 4 1 3 12
2 2 3 4 10
1 2 4 16


Output

0 -1 -1 12 

Note

In the first sample testcase, Rick can purchase 4th plan once and then 2nd plan in order to get to get to planet number 2.

### Response

```cpp
#include <bits/stdc++.h>
#pragma GCC optimize("O3")
using namespace std;
template <class T>
using pq = priority_queue<T>;
template <class T>
using pqg = priority_queue<T, vector<T>, greater<T>>;
int scan() { return getchar(); }
template <class T>
void scan(T a) {
  cin >> a;
}
void scan(int &a) { cin >> a; }
void scan(long long &a) { cin >> a; }
void scan(char &a) { cin >> a; }
void scan(double &a) { cin >> a; }
void scan(long double &a) { cin >> a; }
void scan(char a[]) { scanf("%s", a); }
void scan(string &a) { cin >> a; }
template <class T>
void scan(vector<T> &);
template <class T, size_t size>
void scan(array<T, size> &);
template <class T, class L>
void scan(pair<T, L> &);
template <class T, size_t size>
void scan(T (&)[size]);
template <class T>
void scan(vector<T> &a) {
  for (auto &i : a) scan(i);
}
template <class T>
void scan(deque<T> &a) {
  for (auto &i : a) scan(i);
}
template <class T, size_t size>
void scan(array<T, size> &a) {
  for (auto &i : a) scan(i);
}
template <class T, class L>
void scan(pair<T, L> &p) {
  scan(p.first);
  scan(p.second);
}
template <class T, size_t size>
void scan(T (&a)[size]) {
  for (auto &i : a) scan(i);
}
template <class T>
void scan(T &a) {
  cin >> a;
}
void IN() {}
template <class Head, class... Tail>
void IN(Head &head, Tail &...tail) {
  scan(head);
  IN(tail...);
}
string stin() {
  string s;
  cin >> s;
  return s;
}
template <class T, class S>
inline bool chmax(T &a, S b) {
  if (a < b) {
    a = b;
    return 1;
  }
  return 0;
}
template <class T, class S>
inline bool chmin(T &a, S b) {
  if (a > b) {
    a = b;
    return 1;
  }
  return 0;
}
vector<int> iota(int n) {
  vector<int> a(n);
  iota(begin(a), end(a), 0);
  return a;
}
template <class T>
void UNIQUE(vector<T> &x) {
  sort(begin(x), end(x));
  x.erase(unique(begin(x), end(x)), x.end());
}
int in() {
  int x;
  cin >> x;
  return x;
}
long long lin() {
  unsigned long long x;
  cin >> x;
  return x;
}
void print() { putchar(' '); }
void print(bool a) { cout << a; }
void print(int a) { cout << a; }
void print(long long a) { cout << a; }
void print(char a) { cout << a; }
void print(string &a) { cout << a; }
void print(double a) { cout << a; }
template <class T>
void print(const vector<T> &);
template <class T, size_t size>
void print(const array<T, size> &);
template <class T, class L>
void print(const pair<T, L> &p);
template <class T, size_t size>
void print(const T (&)[size]);
template <class T>
void print(const vector<T> &a) {
  if (a.empty()) return;
  print(a[0]);
  for (auto i = a.begin(); ++i != a.end();) {
    cout << " ";
    print(*i);
  }
  cout << endl;
}
template <class T>
void print(const deque<T> &a) {
  if (a.empty()) return;
  print(a[0]);
  for (auto i = a.begin(); ++i != a.end();) {
    cout << " ";
    print(*i);
  }
}
template <class T, size_t size>
void print(const array<T, size> &a) {
  print(a[0]);
  for (auto i = a.begin(); ++i != a.end();) {
    cout << " ";
    print(*i);
  }
}
template <class T, class L>
void print(const pair<T, L> &p) {
  cout << '(';
  print(p.first);
  cout << ",";
  print(p.second);
  cout << ')';
}
template <class T>
void print(set<T> &x) {
  for (auto e : x) print(e), cout << " ";
  cout << endl;
}
template <class T>
void print(multiset<T> &x) {
  for (auto e : x) print(e), cout << " ";
  cout << endl;
}
template <class T, size_t size>
void print(const T (&a)[size]) {
  print(a[0]);
  for (auto i = a; ++i != end(a);) {
    cout << " ";
    print(*i);
  }
}
template <class T>
void print(const T &a) {
  cout << a;
}
int out() {
  putchar('\n');
  return 0;
}
template <class T>
int out(const T &t) {
  print(t);
  putchar('\n');
  return 0;
}
template <class Head, class... Tail>
int out(const Head &head, const Tail &...tail) {
  print(head);
  putchar(' ');
  out(tail...);
  return 0;
}
long long gcd(long long a, long long b) {
  while (b) {
    long long c = b;
    b = a % b;
    a = c;
  }
  return a;
}
long long lcm(long long a, long long b) {
  if (!a || !b) return 0;
  return a * b / gcd(a, b);
}
vector<pair<long long, long long>> factor(long long x) {
  vector<pair<long long, long long>> ans;
  for (long long i = 2; i * i <= x; i++)
    if (x % i == 0) {
      ans.push_back({i, 1});
      while ((x /= i) % i == 0) ans.back().second++;
    }
  if (x != 1) ans.push_back({x, 1});
  return ans;
}
vector<int> divisor(int x) {
  vector<int> ans;
  for (int i = 1; i * i <= x; i++)
    if (x % i == 0) {
      ans.push_back(i);
      if (i * i != x) ans.push_back(x / i);
    }
  return ans;
}
template <typename T>
void zip(vector<T> &x) {
  vector<T> y = x;
  sort(begin(y), end(y));
  for (int i = 0; i < x.size(); ++i) {
    x[i] = distance((y).begin(), lower_bound(begin(y), end(y), (x[i])));
  }
}
int popcount(long long x) { return __builtin_popcountll(x); }
mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
int rnd(int n) { return uniform_int_distribution<int>(0, n - 1)(rng); }
template <typename T>
void shuffle(vector<T> &v) {
  for (long long i = v.size() - 1; i >= 1; --i) {
    swap(v[i], v[rnd(i)]);
  }
}
vector<string> YES{"NO", "YES"};
vector<string> Yes{"No", "Yes"};
vector<string> yes{"no", "yes"};
template <class... T>
void err(const T &...) {}
template <typename T>
struct edge {
  int from, to;
  T cost;
  int id;
  edge(int to, T cost) : from(-1), to(to), cost(cost) {}
  edge(int from, int to, T cost) : from(from), to(to), cost(cost) {}
  edge &operator=(const int &x) {
    to = x;
    return *this;
  }
  operator int() const { return to; }
};
template <typename T>
using Edges = vector<edge<T>>;
template <typename T>
using WeightedTree = vector<Edges<T>>;
template <typename T>
using Edges = vector<edge<T>>;
template <typename T>
using WeightedGraph = vector<Edges<T>>;
template <typename T>
using Matrix = vector<vector<T>>;
using Graph = vector<vector<int>>;
using tree = vector<vector<int>>;
tree getTree(int n, int offset = 1) {
  tree res(n);
  for (int i = 0; i < n - 1; i++) {
    int a, b;
    cin >> a >> b;
    a -= offset, b -= offset;
    res[a].emplace_back(b);
    res[b].emplace_back(a);
  }
  return res;
}
template <typename T>
WeightedTree<T> getWeightedTree(int n, int offset = 1) {
  WeightedTree<T> res(n);
  for (int i = 0; i < n - 1; i++) {
    int a, b;
    cin >> a >> b;
    a -= offset, b -= offset;
    T c;
    cin >> c;
    res[a].emplace_back(b, c);
    res[b].emplace_back(a, c);
  }
  return res;
}
Graph getGraph(int n, int m, int offset = 1) {
  Graph res(n);
  for (int i = 0; i < m; ++i) {
    int a, b;
    cin >> a >> b;
    a -= offset, b -= offset;
    res[a].emplace_back(b);
    res[b].emplace_back(a);
  }
  return res;
}
template <typename T>
WeightedGraph<T> getWeightedGraph(int n, int m, int offset = 1) {
  WeightedGraph<T> res(n);
  for (int i = 0; i < m; ++i) {
    int a, b;
    cin >> a >> b;
    T c;
    cin >> c;
    res[a].emplace_back(b, c);
    res[b].emplace_back(a, c);
  }
}
struct Setup_io {
  Setup_io() {
    ios_base::sync_with_stdio(0), cin.tie(0), cout.tie(0);
    cout << fixed << setprecision(15);
  }
} setup_io;
template <typename T>
vector<T> dijkstra(WeightedGraph<T> &g, int s) {
  const auto INF = numeric_limits<T>::max();
  vector<T> d(g.size(), INF);
  using P = pair<T, int>;
  priority_queue<P, vector<P>, greater<P>> pq;
  d[s] = 0;
  pq.emplace(0, s);
  while (!pq.empty()) {
    auto [cost, now] = pq.top();
    pq.pop();
    if (d[now] < cost) continue;
    for (auto &e : g[now]) {
      if (d[e] <= d[now] + e.cost) continue;
      d[e] = d[now] + e.cost;
      pq.emplace(d[e], e.to);
    }
  }
  return d;
}
int main() {
  int n, q, s;
  IN(n, q, s);
  int N = 1;
  while (N < n) {
    N <<= 1;
  }
  WeightedGraph<long long> g(N * 4 + n);
  while (q--) {
    int id;
    IN(id);
    if (id == 1) {
      int v, u, w;
      IN(v, u, w);
      g[v - 1].emplace_back(u - 1, w);
    }
    if (id == 2) {
      int v, l, r, w;
      IN(v, l, r, w);
      l--;
      for (int d = r - l; d >= 1; d = r - l) {
        int L = l | ((1U << 31) >> __builtin_clz(d));
        int k = __builtin_ctz(L);
        g[v - 1].emplace_back(((N | l) >> k) + n, w);
        l += L & (-L);
      }
    }
    if (id == 3) {
      int v, l, r, w;
      IN(v, l, r, w);
      l--;
      for (int d = r - l; d >= 1; d = r - l) {
        int L = l | ((1U << 31) >> __builtin_clz(d));
        int k = __builtin_ctz(L);
        g[((N | l) >> k) + n + N * 2].emplace_back(v - 1, w);
        l += L & (-L);
      }
    }
  }
  for (long long i = 0; i < N - 1; ++i) {
    g[n + i].emplace_back(n + i * 2, 0);
    g[n + i].emplace_back(n + i * 2 + 1, 0);
  }
  for (long long i = 0; i < N - 1; ++i) {
    g[n + N * 2 + i * 2].emplace_back(n + N * 2 + i, 0);
    g[n + N * 2 + i * 2 + 1].emplace_back(n + N * 2 + i, 0);
  }
  for (long long i = 0; i < n; ++i) {
    g[n + N + i].emplace_back(i, 0);
    g[i].emplace_back(n + N * 3 + i, 0);
  }
  auto d = dijkstra(g, s - 1);
  for (long long i = 0; i < n; ++i) {
    if (d[i] == LLONG_MAX)
      cout << -1;
    else
      cout << d[i];
    cout << " ";
  }
  cout << '\n';
}

```