#include <bits/stdc++.h>
using namespace std;
const int N = 1000007;
const int mod = 1e9 + 7;
const int inf = 0x3f3f3f3f3f3f3f3f;
const double eps = 1e-8;
int dx[4] = {-1, 0, 1, 0};
int dy[4] = {0, 1, 0, -1};
int n, m, k, t, q, p;
int vis[N], b[N];
struct Node {
  int w, l, r;
} a[N];
bool cmp(Node a, Node b) { return a.w < b.w; }
struct tree {
  int l, r, v, add;
} 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].add != 0) {
    tr[u << 1].add += tr[u].add;
    tr[u << 1 | 1].add += tr[u].add;
    tr[u << 1].v += tr[u].add;
    tr[u << 1 | 1].v += tr[u].add;
    tr[u].add = 0;
  }
}
void build(int u, int l, int r) {
  tr[u].l = l, tr[u].r = r;
  tr[u].add = 0;
  if (l == r) {
    tr[u].v = 0;
    return;
  }
  int mid = l + r >> 1;
  if (l <= mid) build(u << 1, l, mid);
  if (r > mid) build(u << 1 | 1, mid + 1, r);
  pushup(u);
}
void modify2(int u, int l, int r, int w) {
  if (l > r) return;
  if (l <= tr[u].l && r >= tr[u].r) {
    tr[u].add += w;
    tr[u].v += w;
    return;
  }
  pushdown(u);
  int mid = tr[u].l + tr[u].r >> 1;
  if (l <= mid) modify2(u << 1, l, r, w);
  if (r > mid) modify2(u << 1 | 1, l, r, w);
  pushup(u);
}
int query(int u, int l, int r) {
  if (l <= tr[u].l && r >= tr[u].r) {
    return tr[u].v;
  }
  int mid = tr[u].l + tr[u].r >> 1;
  int res = inf;
  if (l <= mid) res = min(res, query(u << 1, l, r));
  if (r > mid) res = min(res, query(u << 1 | 1, l, r));
  return res;
}
signed main() {
  cin >> n >> m;
  int cnt = 0;
  int maxm = 0;
  for (int i = 1; i <= n; i++) {
    int l, r, w;
    cin >> l >> r >> w;
    maxm = max(maxm, r);
    r--;
    a[++cnt] = {w, l, r};
  }
  n = cnt;
  sort(a + 1, a + 1 + n, cmp);
  build(1, 1, maxm);
  int res = inf;
  for (int i = 1, j = 0; i <= n; i++) {
    while (j < n && query(1, 1, m - 1) <= 0) {
      j++;
      modify2(1, a[j].l, a[j].r, 1);
    }
    if (query(1, 1, m - 1) >= 1) res = min(res, a[j].w - a[i].w);
    if (i == n) break;
    modify2(1, a[i].l, a[i].r, -1);
  }
  cout << res << "\n";
  return 0;
}

### Prompt

In Cpp, your task is to solve 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;
const int N = 1000007;
const int mod = 1e9 + 7;
const int inf = 0x3f3f3f3f3f3f3f3f;
const double eps = 1e-8;
int dx[4] = {-1, 0, 1, 0};
int dy[4] = {0, 1, 0, -1};
int n, m, k, t, q, p;
int vis[N], b[N];
struct Node {
  int w, l, r;
} a[N];
bool cmp(Node a, Node b) { return a.w < b.w; }
struct tree {
  int l, r, v, add;
} 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].add != 0) {
    tr[u << 1].add += tr[u].add;
    tr[u << 1 | 1].add += tr[u].add;
    tr[u << 1].v += tr[u].add;
    tr[u << 1 | 1].v += tr[u].add;
    tr[u].add = 0;
  }
}
void build(int u, int l, int r) {
  tr[u].l = l, tr[u].r = r;
  tr[u].add = 0;
  if (l == r) {
    tr[u].v = 0;
    return;
  }
  int mid = l + r >> 1;
  if (l <= mid) build(u << 1, l, mid);
  if (r > mid) build(u << 1 | 1, mid + 1, r);
  pushup(u);
}
void modify2(int u, int l, int r, int w) {
  if (l > r) return;
  if (l <= tr[u].l && r >= tr[u].r) {
    tr[u].add += w;
    tr[u].v += w;
    return;
  }
  pushdown(u);
  int mid = tr[u].l + tr[u].r >> 1;
  if (l <= mid) modify2(u << 1, l, r, w);
  if (r > mid) modify2(u << 1 | 1, l, r, w);
  pushup(u);
}
int query(int u, int l, int r) {
  if (l <= tr[u].l && r >= tr[u].r) {
    return tr[u].v;
  }
  int mid = tr[u].l + tr[u].r >> 1;
  int res = inf;
  if (l <= mid) res = min(res, query(u << 1, l, r));
  if (r > mid) res = min(res, query(u << 1 | 1, l, r));
  return res;
}
signed main() {
  cin >> n >> m;
  int cnt = 0;
  int maxm = 0;
  for (int i = 1; i <= n; i++) {
    int l, r, w;
    cin >> l >> r >> w;
    maxm = max(maxm, r);
    r--;
    a[++cnt] = {w, l, r};
  }
  n = cnt;
  sort(a + 1, a + 1 + n, cmp);
  build(1, 1, maxm);
  int res = inf;
  for (int i = 1, j = 0; i <= n; i++) {
    while (j < n && query(1, 1, m - 1) <= 0) {
      j++;
      modify2(1, a[j].l, a[j].r, 1);
    }
    if (query(1, 1, m - 1) >= 1) res = min(res, a[j].w - a[i].w);
    if (i == n) break;
    modify2(1, a[i].l, a[i].r, -1);
  }
  cout << res << "\n";
  return 0;
}

```