Game Routes - Algorithm

$1.$ Run Kahn's algorithm to get the topological order of the levels.

$2.$ Initialize ways[1] = 1 and all other ways[i] = 0.

$3.$ Process levels in topological order.

For each level $u$: For each neighbor $v$ where edge $u \to v$ exists: ways[v] = (ways[v] + ways[u]) % 10^9 + 7.

$4.$ After processing all levels, the answer is ways[n].

Why modulo? Because the number of paths can be exponentially large. The problem asks for the result modulo $10^9 + 7$ to keep numbers manageable.

This runs in $O(V + E)$ time and uses $O(V)$ space.