Haunted Mansion: The Shortest Path

You are trapped in a haunted mansion consisting of n rooms connected by m corridors. Each corridor connects two rooms and has two attributes: its length d and an accessibility flag a (where a = 1 means the corridor is accessible and a = 0 means it is blocked).

Your task is to determine the shortest path from room 1 to room n using only accessible corridors. If there exists no path from room 1 to room n through accessible corridors, output IMPOSSIBLE.

Note: Use \(\LaTeX\) format for all formulas. For example, the distance from room 1 to room n is given by \(d(1, n)\), which should be minimized.

inputFormat

The first line contains two integers n and m, where n is the number of rooms and m is the number of corridors.

Each of the following m lines contains four integers: u, v, d, and a. Here, u and v denote the rooms connected by the corridor, d represents the length of the corridor, and a is the accessibility flag (1 if accessible, 0 if blocked).

outputFormat

Output a single line with the minimum distance from room 1 to room n if a valid path exists. Otherwise, output IMPOSSIBLE.

5 6
1 2 2 1
2 3 1 1
3 5 5 0
1 4 1 1
4 5 3 1
2 5 5 1

4