Mercurius-codegen throw error: error TS2304: Cannot find name '_Service'.

I am using @mercuriusjs/federation and mercurius-codegen to build a subgraph. I follow implementation directed by the doc. But always get the following errors

src/__generated-types__.ts:209:33 - error TS2304: Cannot find name '_Service'.

209   _Service: ResolverTypeWrapper<_Service>;
                                    ~~~~~~~~

src/__generated-types__.ts:223:13 - error TS2304: Cannot find name '_Service'.

223   _Service: _Service;
                ~~~~~~~~

src/__generated-types__.ts:277:19 - error TS2304: Cannot find name 'Query_entitiesArgs'.

277     RequireFields<Query_entitiesArgs, "representations">
                      ~~~~~~~~~~~~~~~~~~

src/__generated-types__.ts:356:52 - error TS2304: Cannot find name '_Service'.

356     sdl?: LoaderResolver<Maybe<Scalars["String"]>, _Service, {}, TContext>;

In my code typescript is not angry anywhere.
Here is my server.ts file

import Fastify, { FastifyRequest, FastifyReply } from "fastify";
import mercurius from "mercurius";
import mercuriusCodegen from "mercurius-codegen";
import { buildFederationSchema } from "@mercuriusjs/federation";
//
import { userTypeDefs } from "./user/user.schema";
import { userResolvers } from "./user/user.resolvers";

//###########################################################################

const app = Fastify();

const PORT = 4001;

const buildContext = async (req: FastifyRequest, _reply: FastifyReply) => {
  return {
    authorization: req.headers.authorization,
  };
};

type PromiseType<T> = T extends PromiseLike<infer U> ? U : T;

declare module "mercurius" {
  interface MercuriusContext
    extends PromiseType<ReturnType<typeof buildContext>> {}
}

app.register(mercurius, {
  schema: buildFederationSchema(userTypeDefs, {
    isGateway: false,
  }),
  resolvers: userResolvers,
  context: buildContext,
});

mercuriusCodegen(app, {
  // Commonly relative to your root package.json
  targetPath: "./src/__generated-types__.ts",
  // operationsGlob: "./src/graphql/operations/*.gql",
  // codegenConfig: {
  //   loadersCustomParentTypes: {
  //     Human: "never",
  //   },
  // },
}).catch(console.error);

// Start server
app.get("/", async function (req, reply) {
  const query = "{ _service { sdl } }";
  return app.graphql(query);
});

app.listen({ port: PORT });

I don't know what is going wrong there. I cannot modify generated-types.ts file since it is generated automatically when I start the server.

Start with server.ts, especially the buildFederationSchema setup and the mercuriusCodegen call that writes src/generated-types.ts. Reproduce the TypeScript errors, then inspect the generated definitions around _Service and Query_entitiesArgs; done means the generated file type-checks for this federation setup without manual edits.