Show elements in a text box according to a radio button selected - radio-button

Question

I have this problem: In a form, I want to display the info from a box (idCreditorCnpCui) only if the second or the third option is selected from the form (if "P" or "O" option is selected). While I select any of these options, the box appears as it should. The problem I encountered is that when I press the "sent" button (with O or P option), the idCreditorCnpCui box disappears from the view.
This is the HTML with the options of the form:
<div class="form-field">
<label for="payment.creditorOrganizationOrPerson"><localization:localize key="creditorOrganizationOrPerson.label"/></label>
<div class="form-field-element">
<input type="radio" property="payment.creditorOrganizationOrPerson" value="N" onclick="display();" /> N <br>
</div>
<div class="form-field-element">
<input type="radio" property="payment.creditorOrganizationOrPerson" value="P" onclick="display();" /> P <br>
</div>
<div class="form-field-element">
<input type="radio" property="payment.creditorOrganizationOrPerson" value="O" onclick="display();" /> O
</div>
</div>
This is the box I want to be display or no according the option selected:
<div class="form-field" id="idCreditorCnpCui" style="display:none">
<label for="payment.creditorCnpCui"><localization:localize key="creditorCnpCui.label"/></label>
<div class="form-field-element">
<input type="text" property="payment.creditorCnpCui" size="36" maxlength="35" styleClass="input-field" styleId="payment.creditorCnpCui"/>
</div>
And this is the js
function display(toDisplay,idDiv){
if(toDisplay == false){
document.getElementById(idDiv).style.display = "none";
}else{
document.getElementById(idDiv).style.display = "block";
}
}
display(false,"idCreditorCnpCui");
If I turn the final line to "display(true, "idCreditorCnpCui"), the box appear even when the option "N" is selected by default. That should not happen since the N option means the idCreditorCnpCui box is hidden. Any idea please.
I want a field to be display just if an option is selected. But when I send the form, the field disappears even when the option that display that field is selected