Magento rest api url to retrieve products from specific websites

My setup looks like this

• Default -> Main Store -> MainStoreView
• Website1 -> Store 1 -> StoreView1 Store 2 -> StoreView2

Now I want to know how to retrieve products only from Website1->Store1 or Website1->Store2. I thought of using normal url like www.mysite.com/api/rest/products/ and filter the products by storeId, but the problem is I am not getting any products from Website1. I am getting products only from default website.

Can anyone give any insight into why this is happening?

Looking at: Mage_Catalog_Model_Api2_Product_Rest::_retrieveCollection():

$collection = Mage::getResourceModel('catalog/product_collection');
$store = $this->_getStore();
//[...]
$collection->addStoreFilter($store->getId()) 

So, the collection takes into consideration a store view filter. Let's dig deepr in _getStore() method:

Mage_Api2_Model_Resource::_getStore():

protected function _getStore()
    {
        $store = $this->getRequest()->getParam('store');
        try {
            if ($this->getUserType() != Mage_Api2_Model_Auth_User_Admin::USER_TYPE) {
                // customer or guest role
                if (!$store) {
                    $store = Mage::app()->getDefaultStoreView();
                } else {
                    $store = Mage::app()->getStore($store);
                }
            } else {
                // admin role
                if (is_null($store)) {
                    $store = Mage_Catalog_Model_Abstract::DEFAULT_STORE_ID;
                }
                $store = Mage::app()->getStore($store);
            }
        } catch (Mage_Core_Model_Store_Exception $e) {
            // store does not exist
            $this->_critical('Requested store is invalid', Mage_Api2_Model_Server::HTTP_BAD_REQUEST);
        }
        return $store;
    }

Based on this, I believe you can specify: your_request_url?param...&store=STORE_ID