Java Rest with Jersey and Tomcat error 404

I'm trying to follow a rest tutorial with jersey and tomcat. But I'm getting the 404 error. Can someone help me? Here are my classes and settings:

package com.programmer.gate.JerseyRestService;

import javax.ws.rs.GET;
import javax.ws.rs.Path;
import javax.ws.rs.Produces;
import javax.ws.rs.core.MediaType;

/**
 * Root resource (exposed at "myresource" path)
 */
@Path("myresource")
public class MyResource {

   /**
     * Method handling HTTP GET requests. The returned object will be sent
     * to the client as "text/plain" media type.
     *
     * @return String that will be returned as a text/plain response.
   */
    @GET
    @Produces(MediaType.TEXT_PLAIN)
    public String getIt() {
        return "Got it!";
    }
}

My web.xml:

<?xml version="1.0" encoding="UTF-8"?>
<web-app version="2.5" 
     xmlns="http://java.sun.com/xml/ns/javaee" 
     xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" 
     xsi:schemaLocation="http://java.sun.com/xml/ns/javaee 
http://java.sun.com/xml/ns/javaee/web-app_2_5.xsd">
    <servlet>
        <servlet-name>Jersey Web Application</servlet-name>
        <servlet-class>org.glassfish.jersey.servlet.ServletContainer</servlet-class>
        <init-param>
            <param-name>jersey.config.server.provider.packages</param-name>
            <param-value>com.programmer.gate.JerseyRestService</param-value>
        </init-param>
        <load-on-startup>1</load-on-startup>
    </servlet>
    <servlet-mapping>
        <servlet-name>Jersey Web Application</servlet-name>
        <url-pattern>/rest/*</url-pattern>
    </servlet-mapping>
</web-app>

and my pom.xml

<project xmlns="http://maven.apache.org/POM/4.0.0" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance"
     xsi:schemaLocation="http://maven.apache.org/POM/4.0.0 http://maven.apache.org/maven-v4_0_0.xsd">

<modelVersion>4.0.0</modelVersion>

<groupId>com.programmer.gate</groupId>
<artifactId>JerseyRestService</artifactId>
<packaging>war</packaging>
<version>0.0.1-SNAPSHOT</version>
<name>JerseyRestService</name>

<build>
    <finalName>JerseyRestService</finalName>
    <plugins>
        <plugin>
            <groupId>org.apache.maven.plugins</groupId>
            <artifactId>maven-compiler-plugin</artifactId>
            <version>2.5.1</version>
            <inherited>true</inherited>
            <configuration>
                <source>1.7</source>
                <target>1.7</target>
            </configuration>
        </plugin>
    </plugins>
</build>

<dependencyManagement>
    <dependencies>
        <dependency>
            <groupId>org.glassfish.jersey</groupId>
            <artifactId>jersey-bom</artifactId>
            <version>${jersey.version}</version>
            <type>pom</type>
            <scope>import</scope>
        </dependency>
    </dependencies>
</dependencyManagement>

<dependencies>
    <dependency>
        <groupId>org.glassfish.jersey.containers</groupId>
        <artifactId>jersey-container-servlet-core</artifactId>
        <!-- use the following artifactId if you don't need servlet 2.x compatibility -->
        <!-- artifactId>jersey-container-servlet</artifactId -->
    </dependency>
    <dependency>
        <groupId>org.glassfish.jersey.inject</groupId>
        <artifactId>jersey-hk2</artifactId>
    </dependency>
    <!-- uncomment this to get JSON support
    <dependency>
        <groupId>org.glassfish.jersey.media</groupId>
        <artifactId>jersey-media-json-binding</artifactId>
    </dependency>
    -->
</dependencies>
<properties>
    <jersey.version>2.27</jersey.version>
    <project.build.sourceEncoding>UTF-8</project.build.sourceEncoding>
</properties>

I'm right-clicking - > run as - > run on server Access link

But you do not find my appeal. Can someone help me?