Number of shortest paths from any particular node to all nodes using bFS

auto bfs(int s)
{
    vi dist(n + 1, INF), paths(n + 1, 0);
    dist[s] = 0;
    paths[s] = 1;
    queue<int> q;
    q.push(s);
    while (!q.empty())
    {
        int u = q.front();
        q.pop();
        for (int v : adj[u])
        {
            if (dist[v] > dist[u] + 1)
            {
                dist[v] = dist[u] + 1;
                paths[v] = paths[u];
                q.push(v);
            }
            else if (dist[v] == dist[u] + 1)
            {
                paths[v] += paths[u];
            }
        }
    }
    return make_pair(dist, paths);
}