import sys import heapq from collections import defaultdict def main(): input = sys.stdin.read().split() idx = 0 N, M = int(input[idx]), int(input[idx+1]) idx +=2 edges = [[] for _ in range(N+1)] edge_info = {} for _ in range(M): u = int(input[idx]) v = int(input[idx+1]) c = int(input[idx+2]) d = int(input[idx+3]) idx +=4 edges[u].append((v, c, d)) edges[v].append((u, c, d)) if (u, v) not in edge_info: edge_info[(u, v)] = (c, d) if (v, u) not in edge_info: edge_info[(v, u)] = (c, d) # Function to run Dijkstra and return the shortest path cost and the edges used def dijkstra(start, end, graph, track_edges=False): dist = [float('inf')] * (N+1) dist[start] = 0 parent = [[] for _ in range(N+1)] heap = [(0, start)] heapq.heapify(heap) while heap: current_dist, u = heapq.heappop(heap) if u == end: break if current_dist > dist[u]: continue for (v, c, d) in graph[u]: if dist[v] > current_dist + c: dist[v] = current_dist + c parent[v] = [(u, (u, v, c, d))] heapq.heappush(heap, (dist[v], v)) elif dist[v] == current_dist + c: parent[v].append((u, (u, v, c, d))) if dist[end] == float('inf'): return (float('inf'), set()) if track_edges else float('inf') if not track_edges: return dist[end] # Backtrack to find edges used in the shortest path visited = set() edge_set = set() q = [end] while q: v = q.pop() if v in visited: continue visited.add(v) for (u, e) in parent[v]: edge = (min(u, e[1]), max(u, e[1])) edge_set.add(edge) q.append(u) return (dist[end], edge_set) # Get the shortest path S1 and the edges used s1, edges_s1 = dijkstra(1, N, edges, track_edges=True) if s1 == float('inf'): print(-1) return # Function to create a new graph by removing edges in edges_s1 def remove_edges(original_edges, edges_to_remove): new_edges = [[] for _ in range(N+1)] for u in range(1, N+1): for (v, c, d) in original_edges[u]: edge = (min(u, v), max(u, v)) if edge not in edges_to_remove: new_edges[u].append((v, c, d)) return new_edges # Compute candidate1: remove edges in s1 and find path from N to 1 graph_removed = remove_edges(edges, edges_s1) candidate1 = dijkstra(N, 1, graph_removed, track_edges=False) # Function to create a new graph where edges in edges_s1 have their cost changed to d def modify_edges(original_edges, edges_to_modify): new_edges = [[] for _ in range(N+1)] for u in range(1, N+1): for (v, c, d) in original_edges[u]: edge = (min(u, v), max(u, v)) if edge in edges_to_modify: new_edges[u].append((v, d, d)) else: new_edges[u].append((v, c, d)) return new_edges # Compute candidate2: modify edges in s1 to d and find path from N to 1 graph_modified = modify_edges(edges, edges_s1) candidate2 = dijkstra(N, 1, graph_modified, track_edges=False) # Calculate possible answers min_total = float('inf') if candidate1 != float('inf'): min_total = s1 + candidate1 if candidate2 != float('inf'): min_total = min(min_total, s1 + candidate2) print(min_total if min_total != float('inf') else -1) if __name__ == '__main__': main()