Single Source Longest Path

Given a weighted acyclic directed graph (DAG) with positive integer weights, and two nodes in the graph i, j, find the longest path from node i -> node j.

Input format:
line 1: [number of nodes N] [number of edges M]
line 2: i j
line 3 to M+2: [node1] [node2] [weight of edge node1->node2]

note: The graph nodes are labeled 0, 1, 2, ..., N-1; all weights are positive integers between 1 and 10000

Example 1

Input:
4 5
0 3
0 1 10
0 2 20
1 3 30
2 3 15
0 3 60
Output:
60
Explanation:
see the picture below; the longest path from node 0 to node 3 is 60.