如何上传pdf到flutter的firebase存储？

import 'package:firebase_storage/firebase_storage.dart';

FirebaseStorage storage = FirebaseStorage.instance;

File pdfFile = File('path_to_pdf_file.pdf');
String fileName = 'pdf_file_name.pdf';

Reference ref = storage.ref().child(fileName);
UploadTask uploadTask = ref.putFile(pdfFile);

uploadTask.snapshotEvents.listen((TaskSnapshot snapshot) {
  print('Upload progress: ${snapshot.bytesTransferred}/${snapshot.totalBytes}');
}, onError: (Object e) {
  print('Upload error: $e');
}, onDone: () {
  print('Upload complete');
});

String downloadURL = await ref.getDownloadURL();
print('PDF download URL: $downloadURL');