sse server does not process endpoint correctly when sse path is not a directory

src/commonMain/kotlin/io/modelcontextprotocol/kotlin/sdk/client/SSEClientTransport.kt

@@ -39,7 +39,18 @@ public class SseClientTransport(
     private var job: Job? = null
 
     private val baseUrl by lazy {
-        session.call.request.url.toString().removeSuffix("/")
+        val requestUrl = session.call.request.url.toString()
+        val url = Url(requestUrl)
+        var path = url.encodedPath
+        if (path.isEmpty()) {
+            url.protocolWithAuthority
+        } else if (path.endsWith("/")) {
+            url.protocolWithAuthority + path.removeSuffix("/")
+        } else {
+            // the last item is not a directory, so will not be taken into account
+            path = path.substring(0, path.lastIndexOf("/"))
+            url.protocolWithAuthority + path
+        }
     }
 
     override suspend fun start() {
@@ -79,8 +90,7 @@ public class SseClientTransport(
                             val eventData = event.data ?: ""
 
                             // check url correctness
-                            val maybeEndpoint = Url("$baseUrl/$eventData")
-
+                            val maybeEndpoint = Url("$baseUrl/${if (eventData.startsWith("/")) eventData.substring(1) else eventData}")
                             endpoint.complete(maybeEndpoint.toString())
                         } catch (e: Exception) {
                             _onError(e)

src/jvmTest/kotlin/client/SseTransportTest.kt

@@ -82,4 +82,68 @@ class SseTransportTest : BaseTransportTest() {
         testClientRead(client)
         server.stop()
     }
+
+    @Test
+    fun `test sse path not root path`() = runTest {
+        val server = embeddedServer(CIO, port = PORT) {
+            install(io.ktor.server.sse.SSE)
+            val transports = ConcurrentMap<String, SseServerTransport>()
+            routing {
+                sse("/sse") {
+                    mcpSseTransport("/messages", transports).apply {
+                        onMessage {
+                            send(it)
+                        }
+
+                        start()
+                    }
+                }
+
+                post("/messages") {
+
+                    mcpPostEndpoint(transports)
+                }
+            }
+        }.start(wait = false)
+
+        val client = HttpClient {
+            install(SSE)
+        }.mcpSseTransport {
+            url {
+                host = "localhost"
+                port = PORT
+                pathSegments = listOf("sse")
+            }
+        }
+
+        testClientRead(client)
+        server.stop()
+    }
+
+    @Test
+    fun `test sse path not root path`() = runTest {
+        val server = embeddedServer(CIO, port = PORT) {
+            install(io.ktor.server.sse.SSE)
+            routing {
+                mcpSseTransport(path = "/sse", incomingPath = "/messages") {
+                    onMessage = {
+                        send(it)
+                    }
+                }
+            }
+        }.start(wait = false)
+
+        val client = HttpClient {
+            install(SSE)
+        }.mcpSseTransport {
+            url {
+                host = "localhost"
+                port = PORT
+                pathSegments = listOf("sse")
+            }
+        }
+
+        testClientRead(client)
+        server.stop()
+    }
 }