Cheapest Flights Within K Stops

DESCRIPTION (inspired by Leetcode.com)

A travel booking system needs to find the lowest-cost route between airports. You're given n cities connected by flights, where each flight [from, to, price] represents a direct route with its cost.

Find the cheapest route from src to dst that uses at most k layovers (intermediate cities). If no such route exists, return -1.

Note: A route with k layovers means visiting k intermediate cities, or equivalently, taking k+1 flights.

Example 1:

Input:

n = 4
flights = [[0,1,100], [1,2,100], [2,3,100], [0,3,500]]
src = 0
dst = 3
k = 1

Output:

500

Explanation: The route 0→1→2→3 costs $300 with 2 layovers (cities 1 and 2), which exceeds k=1. The direct flight 0→3 costs $500 with 0 layovers. Even though it's more expensive, it's the only valid route.

Example 2:

Input:

n = 4
flights = [[0,1,100], [1,2,100], [2,3,100]]
src = 0
dst = 3
k = 1

Output:

-1

Explanation: The only path 0→1→2→3 requires 2 layovers (cities 1 and 2), but we're limited to k=1. No valid route exists.