<Edge Case/>

// Problem E · Stress-testing Dijkstra under extreme bounds
// N <= 2e5, M <= 5e5, edge weights up to 1e9 (avoid overflow!)
priority_queue<pair<ll,int>, vector<pair<ll,int>>, greater<>> pq;
dist[1] = 0; pq.push({0, 1});
while (!pq.empty()) {
    auto [d, u] = pq.top(); pq.pop();
    if (d > dist[u]) continue; // prune stale states
    for (auto [v, w] : adj[u]) {
        if (dist[u] + w < dist[v]) {
            pq.push({dist[v] = dist[u] + w, v});
        }
    }
}