Runner's Problem

4000ms

262144K

Description:

You are running through a rectangular field. This field can be represented as a matrix with 3 rows and m columns. (i, j) denotes a cell belonging to i-th row and j-th column.

You start in (2, 1) and have to end your path in (2, m). From the cell (i, j) you may advance to:

(i - 1, j + 1) — only if i > 1,
(i, j + 1), or
(i + 1, j + 1) — only if i < 3.

However, there are n obstacles blocking your path. k-th obstacle is denoted by three integers a_k, l_k and r_k, and it forbids entering any cell (a_k, j) such that l_k ≤ j ≤ r_k.

You have to calculate the number of different paths from (2, 1) to (2, m), and print it modulo 10⁹ + 7.

Input:

The first line contains two integers n and m (1 ≤ n ≤ 10⁴, 3 ≤ m ≤ 10¹⁸) — the number of obstacles and the number of columns in the matrix, respectively.

Then n lines follow, each containing three integers a_k, l_k and r_k (1 ≤ a_k ≤ 3, 2 ≤ l_k ≤ r_k ≤ m - 1) denoting an obstacle blocking every cell (a_k, j) such that l_k ≤ j ≤ r_k. Some cells may be blocked by multiple obstacles.

Output:

Print the number of different paths from (2, 1) to (2, m), taken modulo 10⁹ + 7. If it is impossible to get from (2, 1) to (2, m), then the number of paths is 0.

Sample Input:

2 5
1 3 4
2 2 3

Sample Output:

Informação

Provedor Codeforces

Código CF954F