def path_to_friend(network, user_A, user_B, if path is None: path = []):
    if user_A not in network['connection'] or user_B not in network['connection']:
        return None
    if user_A == user_B:
            return path.append(user_A)
    else:
        path = path + [user_A]
        for connection in network['connection'][user_A]:
            if connection not in path:
                path_to_friend(network, connection, user_B, path)
            if path[-1] == user_B:
                return path
        path.pop()
    return None