#include <bits/stdc++.h>
template <typename T>
inline void rd(T& x) {
  int si = 1;
  char c = getchar();
  x = 0;
  while (!isdigit(c)) si = c == '-' ? -1 : si, c = getchar();
  while (isdigit(c)) x = x * 10 + c - 48, c = getchar();
  x *= si;
}
template <typename T, typename... Args>
inline void rd(T& x, Args&... args) {
  rd(x);
  rd(args...);
}
const int N = 1e6 + 5, Inf = 0x3f3f3f3f, Mod = 998244353;
const long long InfLL = 0x3f3f3f3f3f3f3f3fLL;
int seg[N << 3], tag[N << 3];
void Update(int o) { seg[o] = std::min(seg[o << 1], seg[o << 1 | 1]); }
void PushTag(int o) {
  if (tag[o]) {
    seg[o << 1] += tag[o];
    seg[o << 1 | 1] += tag[o];
    tag[o << 1] += tag[o];
    tag[o << 1 | 1] += tag[o];
    tag[o] = 0;
  }
}
void Modify(int o, int l, int r, int ql, int qr, int v) {
  if (ql > qr) return;
  if (ql <= l && r <= qr)
    seg[o] += v, tag[o] += v;
  else {
    int mid = (l + r) >> 1;
    PushTag(o);
    if (ql <= mid) Modify(o << 1, l, mid, ql, qr, v);
    if (qr > mid) Modify(o << 1 | 1, mid + 1, r, ql, qr, v);
    Update(o);
  }
}
struct Seg {
  int l, r;
  long long w;
} I[N];
int main() {
  int test_case_cnt = 1;
  while (test_case_cnt--) {
    int n, m;
    rd(n, m);
    for (int i = 1; i <= n; ++i) {
      rd(I[i].l, I[i].r, I[i].w);
    }
    std::sort(I + 1, I + n + 1,
              [](const Seg& x, const Seg& y) { return x.w < y.w; });
    long long ans = InfLL;
    for (int l = 1, r = 0; l <= n; ++l) {
      while (r + 1 <= n && !seg[1]) {
        ++r;
        Modify(1, 1, m - 1, I[r].l, I[r].r - 1, 1);
      }
      if (seg[1]) {
        ans = std::min(ans, I[r].w - I[l].w);
      }
      Modify(1, 1, m - 1, I[l].l, I[l].r - 1, -1);
    }
    printf("%lld\n", ans);
  }
  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>
template <typename T>
inline void rd(T& x) {
  int si = 1;
  char c = getchar();
  x = 0;
  while (!isdigit(c)) si = c == '-' ? -1 : si, c = getchar();
  while (isdigit(c)) x = x * 10 + c - 48, c = getchar();
  x *= si;
}
template <typename T, typename... Args>
inline void rd(T& x, Args&... args) {
  rd(x);
  rd(args...);
}
const int N = 1e6 + 5, Inf = 0x3f3f3f3f, Mod = 998244353;
const long long InfLL = 0x3f3f3f3f3f3f3f3fLL;
int seg[N << 3], tag[N << 3];
void Update(int o) { seg[o] = std::min(seg[o << 1], seg[o << 1 | 1]); }
void PushTag(int o) {
  if (tag[o]) {
    seg[o << 1] += tag[o];
    seg[o << 1 | 1] += tag[o];
    tag[o << 1] += tag[o];
    tag[o << 1 | 1] += tag[o];
    tag[o] = 0;
  }
}
void Modify(int o, int l, int r, int ql, int qr, int v) {
  if (ql > qr) return;
  if (ql <= l && r <= qr)
    seg[o] += v, tag[o] += v;
  else {
    int mid = (l + r) >> 1;
    PushTag(o);
    if (ql <= mid) Modify(o << 1, l, mid, ql, qr, v);
    if (qr > mid) Modify(o << 1 | 1, mid + 1, r, ql, qr, v);
    Update(o);
  }
}
struct Seg {
  int l, r;
  long long w;
} I[N];
int main() {
  int test_case_cnt = 1;
  while (test_case_cnt--) {
    int n, m;
    rd(n, m);
    for (int i = 1; i <= n; ++i) {
      rd(I[i].l, I[i].r, I[i].w);
    }
    std::sort(I + 1, I + n + 1,
              [](const Seg& x, const Seg& y) { return x.w < y.w; });
    long long ans = InfLL;
    for (int l = 1, r = 0; l <= n; ++l) {
      while (r + 1 <= n && !seg[1]) {
        ++r;
        Modify(1, 1, m - 1, I[r].l, I[r].r - 1, 1);
      }
      if (seg[1]) {
        ans = std::min(ans, I[r].w - I[l].w);
      }
      Modify(1, 1, m - 1, I[l].l, I[l].r - 1, -1);
    }
    printf("%lld\n", ans);
  }
  return 0;
}

```