如何在flutter和firebase中以不同类型的用户登录？

import 'package:firebase_core/firebase_core.dart';
import 'package:firebase_auth/firebase_auth.dart';

void main() async {
  WidgetsFlutterBinding.ensureInitialized();
  await Firebase.initializeApp();
  runApp(MyApp());
}

class LoginPage extends StatefulWidget {
  @override
  _LoginPageState createState() => _LoginPageState();
}

class _LoginPageState extends State<LoginPage> {
  final FirebaseAuth _auth = FirebaseAuth.instance;
  String _email = '';
  String _password = '';

  Future<void> _login() async {
    try {
      UserCredential userCredential = await _auth.signInWithEmailAndPassword(
        email: _email,
        password: _password,
      );
      // 登录成功后的处理逻辑
    } catch (e) {
      // 处理登录失败的情况
    }
  }

  @override
  Widget build(BuildContext context) {
    return Scaffold(
      appBar: AppBar(
        title: Text('登录'),
      ),
      body: Padding(
        padding: EdgeInsets.all(16.0),
        child: Column(
          children: [
            TextField(
              onChanged: (value) {
                setState(() {
                  _email = value;
                });
              },
              decoration: InputDecoration(
                labelText: '邮箱',
              ),
            ),
            TextField(
              onChanged: (value) {
                setState(() {
                  _password = value;
                });
              },
              decoration: InputDecoration(
                labelText: '密码',
              ),
              obscureText: true,
            ),
            RaisedButton(
              onPressed: _login,
              child: Text('登录'),
            ),
          ],
        ),
      ),
    );
  }
}

String _userType = '普通用户';

// ...

DropdownButton<String>(
  value: _userType,
  onChanged: (String newValue) {
    setState(() {
      _userType = newValue;
    });
  },
  items: <String>['普通用户', '管理员'].map<DropdownMenuItem<String>>((String value) {
    return DropdownMenuItem<String>(
      value: value,
      child: Text(value),
    );
  }).toList(),
)

Future<void> _login() async {
  try {
    if (_userType == '普通用户') {
      UserCredential userCredential = await _auth.signInWithEmailAndPassword(
        email: _email,
        password: _password,
      );
      // 普通用户登录成功后的处理逻辑
    } else if (_userType == '管理员') {
      // 管理员登录逻辑
    }
  } catch (e) {
    // 处理登录失败的情况
  }
}