Magento – How to get product ids of specific category and not in other categories in Magento

I want to get product ids of a specific category and product ids not in other categories only in a specific category.

For example,

category ids = 3, 4, 10 and product ids = 10, 12, 14 and category id 3 belong to product id 10 and category id 4 belong to product ids 10, 12, 14 and category id 10 belong to product id 14.

When I filter on category id = 4, it returns product ids 10, 12 and 14, but I want to return only product id 12 because I only want the product id which is not in other categories. In my filter category id 4 returns product ids 10,12 and 14 but I only want to product id 4 because 10 and 14 belong to other categories which I don't want.
I only want to product id 12 in filter. Which filter I used ?

$catIds = array(4);
$notCatIds = array(3, 10);
$productCollection = Mage::getResourceModel('catalog/product_collection')
    ->setStoreId(0)
    ->joinField('category_id', 'catalog/category_product', 'category_id', 'product_id=entity_id', null, 'left')
    ->addAttributeToFilter('category_id', array('in' => $notCatIds))
    ->addAttributeToFilter('category_id', array('in' => $catIds))
    ->addAttributeToFilter('category_id', array('nin' => $notCatIds))
    ->addAttributeToFilter('category_id', array('nin' => array(2)))// 2 is default category id
    ->addAttributeToSelect('*');
$productCollection->getSelect()->group('product_id')->distinct(true);

echo '<pre>';
print_r($productCollection->getData());