Angularjs multiple radio button, auto-select if only one is present - angularjs

Question

Am successful in building angularjs app of multiple dependent radio button.
But have a requirement to default select a radio button if only one is present.
Tried out the stuff in Angularjs: radio button checked, but it doesn't work for multiple radio buttons.
Code Explanation:
HTML Code:
I have two radio buttons. Second set of radio buttons are generated based on the first.
<div>
<ul >
<li> Part One : </li>
<li ng-repeat="f in Input"><input type="radio" name="oneInput" ng-value="f" ng-model="$parent.One"> {{f.Name}} </input></li>
</ul>
</div><br/>
<div>
<ul>
<li> Part Two : </li>
<li ng-repeat="u in filteredUser = (One.User | filter: { Valid: 'Y' })"><input type="radio" name="userInput" ng-value="u" ng-model="$parent.Two"> {{u.Name}} </input></li>
</ul>
</div><br/>
If I select a radio button in first set, and second set has only one radio button, it must be selected by default.
For example, if I select D, I get the D2 radio button which must be selected.
Complete Code # http://plnkr.co/edit/dY2syxNWobxHpiVKIuux?p=preview
Appreciate your response.

Answer 1

please see here: http://plnkr.co/edit/QVvN6rP3wlyxbOJaAGHQ?p=preview
$scope.$watch('One', function(value) {
if (value.Name) {
var users = $filter('filter')($scope.Input, value);
var vaildUsers = $filter('filter')(users[0].User, {
Valid: "Y"
});
if (vaildUsers.length == 1) {
$scope.Two = vaildUsers[0];
} else
{
$scope.Two = {};
}
}
});