#include <bits/stdc++.h>
using namespace std;
int n, m;
struct node {
  int l, r, w;
} a[300010];
bool cmp(node x, node y) { return x.w < y.w; }
int tree[4000010], tag[4000010];
void pushdown(int now) {
  tag[now << 1] += tag[now];
  tag[now << 1 | 1] += tag[now];
  tree[now << 1] += tag[now];
  tree[now << 1 | 1] += tag[now];
  tag[now] = 0;
}
void modify(int now, int l, int r, int ql, int qr, int val) {
  if (ql <= l && qr >= r) {
    tree[now] += val, tag[now] += val;
    return;
  }
  pushdown(now);
  int mid = (l + r) >> 1;
  if (ql <= mid) modify(now << 1, l, mid, ql, qr, val);
  if (mid < qr) modify(now << 1 | 1, mid + 1, r, ql, qr, val);
  tree[now] = min(tree[now << 1], tree[now << 1 | 1]);
}
int main() {
  cin >> n >> m;
  for (int i = 1; i <= n; i++) cin >> a[i].l >> a[i].r >> a[i].w;
  sort(a + 1, a + 1 + n, cmp);
  int lb, rb;
  lb = 1, rb = 1;
  modify(1, 1, m - 1, a[1].l, a[1].r, 1);
  int ans = 114514114;
  while (rb <= n) {
    if (tree[1] > 0) {
      ans = min(ans, a[rb].w - a[lb].w);
      if (ans == 0) {
        cout << 0;
        return 0;
      }
      modify(1, 1, m - 1, a[lb].l, a[lb].r - 1, -1);
      lb++;
    } else {
      rb++;
      if (rb <= n) modify(1, 1, m - 1, a[rb].l, a[rb].r - 1, 1);
    }
  }
  cout << ans << endl;
  return 0;
}

### Prompt

Create a solution in Cpp for 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;
int n, m;
struct node {
  int l, r, w;
} a[300010];
bool cmp(node x, node y) { return x.w < y.w; }
int tree[4000010], tag[4000010];
void pushdown(int now) {
  tag[now << 1] += tag[now];
  tag[now << 1 | 1] += tag[now];
  tree[now << 1] += tag[now];
  tree[now << 1 | 1] += tag[now];
  tag[now] = 0;
}
void modify(int now, int l, int r, int ql, int qr, int val) {
  if (ql <= l && qr >= r) {
    tree[now] += val, tag[now] += val;
    return;
  }
  pushdown(now);
  int mid = (l + r) >> 1;
  if (ql <= mid) modify(now << 1, l, mid, ql, qr, val);
  if (mid < qr) modify(now << 1 | 1, mid + 1, r, ql, qr, val);
  tree[now] = min(tree[now << 1], tree[now << 1 | 1]);
}
int main() {
  cin >> n >> m;
  for (int i = 1; i <= n; i++) cin >> a[i].l >> a[i].r >> a[i].w;
  sort(a + 1, a + 1 + n, cmp);
  int lb, rb;
  lb = 1, rb = 1;
  modify(1, 1, m - 1, a[1].l, a[1].r, 1);
  int ans = 114514114;
  while (rb <= n) {
    if (tree[1] > 0) {
      ans = min(ans, a[rb].w - a[lb].w);
      if (ans == 0) {
        cout << 0;
        return 0;
      }
      modify(1, 1, m - 1, a[lb].l, a[lb].r - 1, -1);
      lb++;
    } else {
      rb++;
      if (rb <= n) modify(1, 1, m - 1, a[rb].l, a[rb].r - 1, 1);
    }
  }
  cout << ans << endl;
  return 0;
}

```