#include <bits/stdc++.h>
using namespace std;
const long long mod = 10000019;
const int maxn = 1e6 + 5;
struct {
  int laz, sum, m;
} tr[maxn * 4];
struct node {
  int l, r, w;
  bool operator<(const node& x) const { return w < x.w; }
} no[1000005];
int n, m;
void pushdown(int a, int b, int x) {
  if (a == b) {
    tr[x].m = tr[x].sum = x;
    return;
  }
  int laz = tr[x].laz, mid = (a + b) / 2;
  tr[x].laz = 0;
  tr[x << 1].sum += (mid - a + 1) * laz;
  tr[x << 1].laz += laz;
  tr[x << 1].m += laz;
  tr[(x << 1) | 1].sum += (b - mid) * laz;
  tr[(x << 1) | 1].laz += laz;
  tr[(x << 1) | 1].m += laz;
}
void pushup(int a, int b, int x) {
  if (a == b) {
    tr[x].m = tr[x].sum = x;
    return;
  }
  tr[x].m = min(tr[x << 1].m, tr[(x << 1) | 1].m);
  tr[x].sum = tr[x << 1].sum + tr[(x << 1) | 1].sum;
}
void upd(int a, int b, int l, int r, int x, int v) {
  if (a >= l && b <= r) {
    tr[x].laz += v;
    tr[x].sum += v * (b - a + 1);
    tr[x].m += v;
    return;
  }
  int m = (a + b) / 2;
  pushdown(a, b, x);
  if (m >= l) upd(a, m, l, r, x << 1, v);
  if (m < r) upd(m + 1, b, l, r, (x << 1) | 1, v);
  pushup(a, b, x);
}
int que(int a, int b, int l, int r, int x) {
  if (a >= l && b <= r) {
    return tr[x].m;
  }
  int m = (a + b) / 2;
  pushdown(a, b, x);
  int res = maxn;
  if (m >= l) res = min(res, que(a, m, l, r, x << 1));
  if (m < r) res = min(res, que(m + 1, b, l, r, (x << 1) | 1));
  return res;
}
bool check(int x) {
  int m = que(1, m, no[x].l, no[x].r, 1);
  if (m > 1) return true;
  return false;
}
void go(int x) { upd(1, m, no[x].l, no[x].r, 1, -1); }
int main() {
  memset(tr, 0, sizeof tr);
  memset(no, 0, sizeof no);
  cin >> n >> m;
  for (int i = 1; i <= n; i++) {
    cin >> no[i].l >> no[i].r >> no[i].w;
  }
  sort(no + 1, no + n + 1);
  int l = 1, r = 1, res = 10000000;
  --m;
  for (l = 1; l <= n; l++) {
    while (r <= n) {
      if (que(1, m, 1, m, 1) < 1) {
        upd(1, m, no[r].l, no[r].r - 1, 1, 1);
        ++r;
      } else
        break;
    }
    if (que(1, m, 1, m, 1) < 1) break;
    res = min(res, no[r - 1].w - no[l].w);
    upd(1, m, no[l].l, no[l].r - 1, 1, -1);
  }
  cout << res << endl;
}

### 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;
const long long mod = 10000019;
const int maxn = 1e6 + 5;
struct {
  int laz, sum, m;
} tr[maxn * 4];
struct node {
  int l, r, w;
  bool operator<(const node& x) const { return w < x.w; }
} no[1000005];
int n, m;
void pushdown(int a, int b, int x) {
  if (a == b) {
    tr[x].m = tr[x].sum = x;
    return;
  }
  int laz = tr[x].laz, mid = (a + b) / 2;
  tr[x].laz = 0;
  tr[x << 1].sum += (mid - a + 1) * laz;
  tr[x << 1].laz += laz;
  tr[x << 1].m += laz;
  tr[(x << 1) | 1].sum += (b - mid) * laz;
  tr[(x << 1) | 1].laz += laz;
  tr[(x << 1) | 1].m += laz;
}
void pushup(int a, int b, int x) {
  if (a == b) {
    tr[x].m = tr[x].sum = x;
    return;
  }
  tr[x].m = min(tr[x << 1].m, tr[(x << 1) | 1].m);
  tr[x].sum = tr[x << 1].sum + tr[(x << 1) | 1].sum;
}
void upd(int a, int b, int l, int r, int x, int v) {
  if (a >= l && b <= r) {
    tr[x].laz += v;
    tr[x].sum += v * (b - a + 1);
    tr[x].m += v;
    return;
  }
  int m = (a + b) / 2;
  pushdown(a, b, x);
  if (m >= l) upd(a, m, l, r, x << 1, v);
  if (m < r) upd(m + 1, b, l, r, (x << 1) | 1, v);
  pushup(a, b, x);
}
int que(int a, int b, int l, int r, int x) {
  if (a >= l && b <= r) {
    return tr[x].m;
  }
  int m = (a + b) / 2;
  pushdown(a, b, x);
  int res = maxn;
  if (m >= l) res = min(res, que(a, m, l, r, x << 1));
  if (m < r) res = min(res, que(m + 1, b, l, r, (x << 1) | 1));
  return res;
}
bool check(int x) {
  int m = que(1, m, no[x].l, no[x].r, 1);
  if (m > 1) return true;
  return false;
}
void go(int x) { upd(1, m, no[x].l, no[x].r, 1, -1); }
int main() {
  memset(tr, 0, sizeof tr);
  memset(no, 0, sizeof no);
  cin >> n >> m;
  for (int i = 1; i <= n; i++) {
    cin >> no[i].l >> no[i].r >> no[i].w;
  }
  sort(no + 1, no + n + 1);
  int l = 1, r = 1, res = 10000000;
  --m;
  for (l = 1; l <= n; l++) {
    while (r <= n) {
      if (que(1, m, 1, m, 1) < 1) {
        upd(1, m, no[r].l, no[r].r - 1, 1, 1);
        ++r;
      } else
        break;
    }
    if (que(1, m, 1, m, 1) < 1) break;
    res = min(res, no[r - 1].w - no[l].w);
    upd(1, m, no[l].l, no[l].r - 1, 1, -1);
  }
  cout << res << endl;
}

```