#include <bits/stdc++.h>
using namespace std;
void err(istream_iterator<string> it) { cerr << endl; }
template <typename T, typename... Args>
void err(istream_iterator<string> it, T a, Args... args) {
  cerr << *it << " = " << a << endl;
  err(++it, args...);
}
const int inf = 0x3f3f3f3f;
const int mod = 1e9 + 7;
const int fx[4][2] = {{0, 1}, {0, -1}, {1, 0}, {-1, 0}};
const int fxx[8][2] = {{0, 1}, {0, -1}, {1, 0},  {-1, 0},
                       {1, 1}, {1, -1}, {-1, 1}, {-1, -1}};
vector<int> t, ps;
void push(int v) {
  t[v * 2] += ps[v];
  ps[v * 2] += ps[v];
  t[v * 2 + 1] += ps[v];
  ps[v * 2 + 1] += ps[v];
  ps[v] = 0;
}
void upd(int v, int tl, int tr, int l, int r, int val) {
  if (l > r) return;
  if (l == tl && r == tr) {
    t[v] += val;
    ps[v] += val;
  } else {
    push(v);
    int tm = (tl + tr) / 2;
    upd(v * 2, tl, tm, l, min(r, tm), val);
    upd(v * 2 + 1, tm + 1, tr, max(tm + 1, l), r, val);
    t[v] = min(t[v * 2], t[v * 2 + 1]);
  }
}
int get() { return t[1]; }
int main() {
  ios::sync_with_stdio(false);
  cin.tie(nullptr);
  int n, m;
  cin >> n >> m;
  vector<tuple<int, int, int>> a;
  for (int i = int(0); i < int(n); i++) {
    int l, r, w;
    cin >> l >> r >> w;
    --l, r -= 2;
    a.emplace_back(w, l, r);
  }
  --m;
  sort((a).begin(), (a).end(),
       [](tuple<int, int, int>& x, tuple<int, int, int>& y) {
         return get<0>(x) < get<0>(y);
       });
  t.resize(4 * m), ps.resize(4 * m);
  --m;
  int ans = inf;
  int j = 0;
  for (int i = int(0); i < int(n); i++) {
    while (j < n && get() == 0) {
      upd(1, 0, m, get<1>(a[j]), get<2>(a[j]), 1);
      ++j;
    }
    if (get() == 0) break;
    ans = min(ans, get<0>(a[j - 1]) - get<0>(a[i]));
    upd(1, 0, m, get<1>(a[i]), get<2>(a[i]), -1);
  }
  cout << ans << "\n";
  return 0;
}

### Prompt

Generate a CPP solution to the following problem:

You are given n segments on a number line, numbered from 1 to n. The i-th segments covers all integer points from l_i to r_i and has a value w_i.

You are asked to select a subset of these segments (possibly, all of them). Once the subset is selected, it's possible to travel between two integer points if there exists a selected segment that covers both of them. A subset is good if it's possible to reach point m starting from point 1 in arbitrary number of moves.

The cost of the subset is the difference between the maximum and the minimum values of segments in it. Find the minimum cost of a good subset.

In every test there exists at least one good subset.

Input

The first line contains two integers n and m (1 ≤ n ≤ 3 ⋅ 10^5; 2 ≤ m ≤ 10^6) — the number of segments and the number of integer points.

Each of the next n lines contains three integers l_i, r_i and w_i (1 ≤ l_i < r_i ≤ m; 1 ≤ w_i ≤ 10^6) — the description of the i-th segment.

In every test there exists at least one good subset.

Output

Print a single integer — the minimum cost of a good subset.

Examples

Input


5 12
1 5 5
3 4 10
4 10 6
11 12 5
10 12 3


Output


3


Input


1 10
1 10 23


Output


0

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
void err(istream_iterator<string> it) { cerr << endl; }
template <typename T, typename... Args>
void err(istream_iterator<string> it, T a, Args... args) {
  cerr << *it << " = " << a << endl;
  err(++it, args...);
}
const int inf = 0x3f3f3f3f;
const int mod = 1e9 + 7;
const int fx[4][2] = {{0, 1}, {0, -1}, {1, 0}, {-1, 0}};
const int fxx[8][2] = {{0, 1}, {0, -1}, {1, 0},  {-1, 0},
                       {1, 1}, {1, -1}, {-1, 1}, {-1, -1}};
vector<int> t, ps;
void push(int v) {
  t[v * 2] += ps[v];
  ps[v * 2] += ps[v];
  t[v * 2 + 1] += ps[v];
  ps[v * 2 + 1] += ps[v];
  ps[v] = 0;
}
void upd(int v, int tl, int tr, int l, int r, int val) {
  if (l > r) return;
  if (l == tl && r == tr) {
    t[v] += val;
    ps[v] += val;
  } else {
    push(v);
    int tm = (tl + tr) / 2;
    upd(v * 2, tl, tm, l, min(r, tm), val);
    upd(v * 2 + 1, tm + 1, tr, max(tm + 1, l), r, val);
    t[v] = min(t[v * 2], t[v * 2 + 1]);
  }
}
int get() { return t[1]; }
int main() {
  ios::sync_with_stdio(false);
  cin.tie(nullptr);
  int n, m;
  cin >> n >> m;
  vector<tuple<int, int, int>> a;
  for (int i = int(0); i < int(n); i++) {
    int l, r, w;
    cin >> l >> r >> w;
    --l, r -= 2;
    a.emplace_back(w, l, r);
  }
  --m;
  sort((a).begin(), (a).end(),
       [](tuple<int, int, int>& x, tuple<int, int, int>& y) {
         return get<0>(x) < get<0>(y);
       });
  t.resize(4 * m), ps.resize(4 * m);
  --m;
  int ans = inf;
  int j = 0;
  for (int i = int(0); i < int(n); i++) {
    while (j < n && get() == 0) {
      upd(1, 0, m, get<1>(a[j]), get<2>(a[j]), 1);
      ++j;
    }
    if (get() == 0) break;
    ans = min(ans, get<0>(a[j - 1]) - get<0>(a[i]));
    upd(1, 0, m, get<1>(a[i]), get<2>(a[i]), -1);
  }
  cout << ans << "\n";
  return 0;
}

```