Verificar intersecçao em Tela JSF

Olá Pessoas, eu sou novo em programação e novo no Fórum. Estou com um exercício de faculdade que não estou conseguindo fazer, preciso criar uma tela chamada Intersecção, que receba 2 intervalos e retorne uma mensagem em tela informando se existe ou não intersecção entre os intervalos.

Este é meu Manager

    @ManagedBean
    @ViewScoped
     public class InterseccaoManaged {

	private List<Integer> valorA = new ArrayList<>();
	private List<Integer> valorB = new ArrayList<>();
	
	private Integer tamanho = 0;
	
	FacesContext context = FacesContext.getCurrentInstance();
	
	public void verificarInterseccao() {
		
		for(int i = 0; i < valorA.size(); i++) {
			for(int j = 0; j < valorB.size(); j++) {
				
				if(valorB.add(j) == valorA.add(i)) {
					tamanho ++;
					
					FacesMessage facesMessage = new FacesMessage("Existe interseção entre as faixas A e B");
					context.addMessage(null, facesMessage);
				}else {
					FacesMessage facesMessage = new FacesMessage("Não há interseção entre as faixas A e B");
					context.addMessage(null, facesMessage);
				}
				
			}
		}
		
	}

Essa Minha Tela

<h:form id="formInterseccao">
			<p:messages severity="info,error,fatal" closable="true"/>
			<div class="ui-fluid">
				
				<p:panelGrid 
					columns="2" 
					columnClasses="ui-grid-col-3,ui-grid-col-3"
					layout="grid">
					
					<h:panelGroup>
					<p:outputLabel value="Faixa A:"/>
					<p:inputNumber value="#{interseccaoManaged.valorA[0]}"/>
					<p:inputNumber value="#{interseccaoManaged.valorA[1]}"/>
					<p:inputNumber value="#{interseccaoManaged.valorA[2]}"/>
					<p:inputNumber value="#{interseccaoManaged.valorA[3]}"/>
				</h:panelGroup>
				
				<h:panelGroup>
					<p:outputLabel value="Faixa B:"/>
					<p:inputNumber value="#{interseccaoManaged.valorB[0]}"/>
					<p:inputNumber value="#{interseccaoManaged.valorB[1]}"/>
					<p:inputNumber value="#{interseccaoManaged.valorB[2]}"/>
					<p:inputNumber value="#{interseccaoManaged.valorB[3]}"/>
				</h:panelGroup>
					
				</p:panelGrid>	
				
				<h:panelGroup layout="block" style="text-align:center">
					<p:commandButton 
						value="Consultar"
						update="@form" 
						action="#{lancamentoManaged.verificarInterseccao}"
						style="width:120px"/>
				</h:panelGroup>
			
			</div>
		</h:form>
	</h:body>

E no momento que eu executo é apresentado o Erro

GRAVE: javax.el.PropertyNotFoundException: /interseccao.xhtml @30,74 value="#{interseccaoManaged.interseccoes[0].valorA}": Target Unreachable, [0] returned null
	at com.sun.faces.facelets.el.TagValueExpression.getType(TagValueExpression.java:100)
	at org.primefaces.util.ComponentUtils.getConverter(ComponentUtils.java:152)
	at org.primefaces.renderkit.InputRenderer.getConvertedValue(InputRenderer.java:199)
	at javax.faces.component.UIInput.getConvertedValue(UIInput.java:1046)
	at javax.faces.component.UIInput.validate(UIInput.java:976)
	at javax.faces.component.UIInput.executeValidate(UIInput.java:1249)
	at javax.faces.component.UIInput.processValidators(UIInput.java:712)
	at javax.faces.component.UIComponentBase.processValidators(UIComponentBase.java:1258)
	at javax.faces.component.UIComponentBase.processValidators(UIComponentBase.java:1258)
	at javax.faces.component.UIForm.processValidators(UIForm.java:253)
	at javax.faces.component.UIComponentBase.processValidators(UIComponentBase.java:1258)
	at javax.faces.component.UIComponentBase.processValidators(UIComponentBase.java:1258)
	at javax.faces.component.UIViewRoot.processValidators(UIViewRoot.java:1195)
	at com.sun.faces.lifecycle.ProcessValidationsPhase.execute(ProcessValidationsPhase.java:76)
	at com.sun.faces.lifecycle.Phase.doPhase(Phase.java:101)
	at com.sun.faces.lifecycle.LifecycleImpl.execute(LifecycleImpl.java:198)
	at javax.faces.webapp.FacesServlet.service(FacesServlet.java:646)
	at org.apache.catalina.core.ApplicationFilterChain.internalDoFilter(ApplicationFilterChain.java:231)
	at org.apache.catalina.core.ApplicationFilterChain.doFilter(ApplicationFilterChain.java:166)
	at org.apache.tomcat.websocket.server.WsFilter.doFilter(WsFilter.java:52)
	at org.apache.catalina.core.ApplicationFilterChain.internalDoFilter(ApplicationFilterChain.java:193)
	at org.apache.catalina.core.ApplicationFilterChain.doFilter(ApplicationFilterChain.java:166)
	at filtro.ConexaoHibernateFilter.doFilter(ConexaoHibernateFilter.java:35)
	at org.apache.catalina.core.ApplicationFilterChain.internalDoFilter(ApplicationFilterChain.java:193)
	at org.apache.catalina.core.ApplicationFilterChain.doFilter(ApplicationFilterChain.java:166)
	at org.apache.catalina.core.StandardWrapperValve.invoke(StandardWrapperValve.java:198)
	at org.apache.catalina.core.StandardContextValve.invoke(StandardContextValve.java:96)
	at org.apache.catalina.authenticator.AuthenticatorBase.invoke(AuthenticatorBase.java:493)
	at org.apache.catalina.core.StandardHostValve.invoke(StandardHostValve.java:140)
	at org.apache.catalina.valves.ErrorReportValve.invoke(ErrorReportValve.java:81)
	at org.apache.catalina.valves.AbstractAccessLogValve.invoke(AbstractAccessLogValve.java:650)
	at org.apache.catalina.core.StandardEngineValve.invoke(StandardEngineValve.java:87)
	at org.apache.catalina.connector.CoyoteAdapter.service(CoyoteAdapter.java:342)
	at org.apache.coyote.http11.Http11Processor.service(Http11Processor.java:800)
	at org.apache.coyote.AbstractProcessorLight.process(AbstractProcessorLight.java:66)
	at org.apache.coyote.AbstractProtocol$ConnectionHandler.process(AbstractProtocol.java:806)
	at org.apache.tomcat.util.net.NioEndpoint$SocketProcessor.doRun(NioEndpoint.java:1498)
	at org.apache.tomcat.util.net.SocketProcessorBase.run(SocketProcessorBase.java:49)
	at java.util.concurrent.ThreadPoolExecutor.runWorker(ThreadPoolExecutor.java:1149)
	at java.util.concurrent.ThreadPoolExecutor$Worker.run(ThreadPoolExecutor.java:624)
	at org.apache.tomcat.util.threads.TaskThread$WrappingRunnable.run(TaskThread.java:61)
	at java.lang.Thread.run(Thread.java:748)
Caused by: javax.el.PropertyNotFoundException: Target Unreachable, [0] returned null
	at org.apache.el.parser.AstValue.getTarget(AstValue.java:124)
	at org.apache.el.parser.AstValue.getType(AstValue.java:58)
	at org.apache.el.ValueExpressionImpl.getType(ValueExpressionImpl.java:174)
	at com.sun.faces.facelets.el.TagValueExpression.getType(TagValueExpression.java:98)
	... 41 more

Se poderem me ajudar.

Desde já agradeço.