#include <bits/stdc++.h>
using namespace std;
long long gcd(long long a, long long b) { return b == 0 ? a : gcd(b, a % b); }
void input() {
  freopen("in.txt", "r", stdin);
  freopen("out.txt", "w", stdout);
}
const int N = 1e6 + 10, M = N * 2, inf = 1e8;
struct Node {
  int l, r, w;
} a[N];
int n, m;
bool com(Node n1, Node n2) { return n1.w < n2.w; }
struct Segment {
  int l, r, v, lazy;
} tr[N * 4];
void pushup(int u) { tr[u].v = min(tr[u << 1].v, tr[u << 1 | 1].v); }
void pushdown(int u) {
  if (tr[u].lazy) {
    tr[u << 1].lazy += tr[u].lazy;
    tr[u << 1 | 1].lazy += tr[u].lazy;
    tr[u << 1].v += tr[u].lazy;
    tr[u << 1 | 1].v += tr[u].lazy;
    tr[u].lazy = 0;
  }
}
void build(int u, int l, int r) {
  tr[u].l = l, tr[u].r = r, tr[u].lazy = 0, tr[u].v = 0;
  if (l == r)
    return;
  else {
    int mid = (l + r) >> 1;
    build(u << 1, l, mid);
    build(u << 1 | 1, mid + 1, r);
  }
}
void update(int u, int l, int r, int v) {
  if (l <= tr[u].l && tr[u].r <= r) {
    tr[u].v += v;
    tr[u].lazy += v;
  } else {
    pushdown(u);
    int mid = (tr[u].l + tr[u].r) >> 1;
    if (l <= mid) update(u << 1, l, r, v);
    if (r > mid) update(u << 1 | 1, l, r, v);
    pushup(u);
  }
}
int query(int u, int l, int r) {
  if (l <= tr[u].l && tr[u].r <= r) {
    return tr[u].v;
  } else {
    pushdown(u);
    int mid = (tr[u].l + tr[u].r) >> 1, ans = 1e9;
    if (l <= mid) ans = min(ans, query(u << 1, l, r));
    if (r > mid) ans = min(ans, query(u << 1 | 1, l, r));
    return ans;
  }
}
int main() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  cin >> n >> m;
  int maxm = m + 10;
  for (int i = 1; i <= n; i++)
    cin >> a[i].l >> a[i].r >> a[i].w, maxm = max(maxm, a[i].r), a[i].r--;
  sort(a + 1, a + n + 1, com);
  build(1, 1, maxm);
  int ans = 1e9;
  for (int i = 1, l = 1; i <= n; i++) {
    update(1, a[i].l, a[i].r, 1);
    while (l <= i && query(1, 1, m - 1)) {
      ans = min(ans, a[i].w - a[l].w);
      update(1, a[l].l, a[l].r, -1);
      l++;
    }
  }
  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;
long long gcd(long long a, long long b) { return b == 0 ? a : gcd(b, a % b); }
void input() {
  freopen("in.txt", "r", stdin);
  freopen("out.txt", "w", stdout);
}
const int N = 1e6 + 10, M = N * 2, inf = 1e8;
struct Node {
  int l, r, w;
} a[N];
int n, m;
bool com(Node n1, Node n2) { return n1.w < n2.w; }
struct Segment {
  int l, r, v, lazy;
} tr[N * 4];
void pushup(int u) { tr[u].v = min(tr[u << 1].v, tr[u << 1 | 1].v); }
void pushdown(int u) {
  if (tr[u].lazy) {
    tr[u << 1].lazy += tr[u].lazy;
    tr[u << 1 | 1].lazy += tr[u].lazy;
    tr[u << 1].v += tr[u].lazy;
    tr[u << 1 | 1].v += tr[u].lazy;
    tr[u].lazy = 0;
  }
}
void build(int u, int l, int r) {
  tr[u].l = l, tr[u].r = r, tr[u].lazy = 0, tr[u].v = 0;
  if (l == r)
    return;
  else {
    int mid = (l + r) >> 1;
    build(u << 1, l, mid);
    build(u << 1 | 1, mid + 1, r);
  }
}
void update(int u, int l, int r, int v) {
  if (l <= tr[u].l && tr[u].r <= r) {
    tr[u].v += v;
    tr[u].lazy += v;
  } else {
    pushdown(u);
    int mid = (tr[u].l + tr[u].r) >> 1;
    if (l <= mid) update(u << 1, l, r, v);
    if (r > mid) update(u << 1 | 1, l, r, v);
    pushup(u);
  }
}
int query(int u, int l, int r) {
  if (l <= tr[u].l && tr[u].r <= r) {
    return tr[u].v;
  } else {
    pushdown(u);
    int mid = (tr[u].l + tr[u].r) >> 1, ans = 1e9;
    if (l <= mid) ans = min(ans, query(u << 1, l, r));
    if (r > mid) ans = min(ans, query(u << 1 | 1, l, r));
    return ans;
  }
}
int main() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  cin >> n >> m;
  int maxm = m + 10;
  for (int i = 1; i <= n; i++)
    cin >> a[i].l >> a[i].r >> a[i].w, maxm = max(maxm, a[i].r), a[i].r--;
  sort(a + 1, a + n + 1, com);
  build(1, 1, maxm);
  int ans = 1e9;
  for (int i = 1, l = 1; i <= n; i++) {
    update(1, a[i].l, a[i].r, 1);
    while (l <= i && query(1, 1, m - 1)) {
      ans = min(ans, a[i].w - a[l].w);
      update(1, a[l].l, a[l].r, -1);
      l++;
    }
  }
  cout << ans << '\n';
  return 0;
}

```