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

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

@@ -12,6 +12,7 @@ import io.ktor.http.HttpHeaders
 import io.ktor.http.Url
 import io.ktor.http.append
 import io.ktor.http.isSuccess
+import io.ktor.http.protocolWithAuthority
 import io.modelcontextprotocol.kotlin.sdk.JSONRPCMessage
 import io.modelcontextprotocol.kotlin.sdk.shared.AbstractTransport
 import io.modelcontextprotocol.kotlin.sdk.shared.McpJson
@@ -24,7 +25,6 @@ import kotlinx.coroutines.SupervisorJob
 import kotlinx.coroutines.cancel
 import kotlinx.coroutines.cancelAndJoin
 import kotlinx.coroutines.launch
-import kotlinx.serialization.encodeToString
 import kotlin.concurrent.atomics.AtomicBoolean
 import kotlin.concurrent.atomics.ExperimentalAtomicApi
 import kotlin.properties.Delegates
@@ -55,7 +55,18 @@ public class SseClientTransport(
     private var job: Job? = null
 
     private val baseUrl by lazy {
-        session.call.request.url.toString().removeSuffix("/sse")
+        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() {
@@ -95,8 +106,7 @@ 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/commonTest/kotlin/io/modelcontextprotocol/kotlin/sdk/client/SseTransportTest.kt

@@ -6,6 +6,7 @@ import io.ktor.server.application.install
 import io.ktor.server.cio.CIO
 import io.ktor.server.engine.embeddedServer
 import io.ktor.server.routing.post
+import io.ktor.server.routing.route
 import io.ktor.server.routing.routing
 import io.ktor.server.sse.sse
 import io.ktor.util.collections.ConcurrentMap
@@ -82,4 +83,43 @@ class SseTransportTest : BaseTransportTest() {
         testClientRead(client)
         server.stopSuspend()
     }
+
+    @Test
+    fun `test sse path not root path`() = runTest {
+        val port = 3007
+        val server = embeddedServer(CIO, port = port) {
+            install(io.ktor.server.sse.SSE)
+            val transports = ConcurrentMap<String, SseServerTransport>()
+            routing {
+                route("/sse") {
+                    sse {
+                        mcpSseTransport("", transports).apply {
+                            onMessage {
+                                send(it)
+                            }
+
+                            start()
+                        }
+                    }
+
+                    post {
+                        mcpPostEndpoint(transports)
+                    }
+                }
+            }
+        }.startSuspend(wait = false)
+
+        val client = HttpClient {
+            install(SSE)
+        }.mcpSseTransport {
+            url {
+                host = "localhost"
+                this.port = port
+                pathSegments = listOf("sse")
+            }
+        }
+
+        testClientRead(client)
+        server.stopSuspend()
+    }
 }