Find document looking inside an object

I have this document:

{
  "_id": ObjectId("xxx"),
  "props": {
     "a": "a1",
     "b": "b2"
   }
}

My query looks like this:

db.collection.find({"$and": [ {"props.a" : "a1"}, {"props.b": "b2"} ]}

I get the elements of the query from GET values:

/api/search?a=a1&b=b1

So, I need a way to generate dinamically my query starting from the GET object...

I thought about something like this:

// Little helper to get the object key name by index
Object.prototype.key = function key(int) { var j = -1; for(var i in this) { j++; if(j==int) { return i; } else { continue; } } }

// My attempt
var query = [],
    i     = 0;

_.each(req.query, function(prop) {

    var key = req.query.key(i);

    query.push({"props." + key: prop});

    i = i + 1;

});

But it does not work...

if I do:

_.each(req.query, function(prop) {

    var key = {};
    key.properties = {};
    key.properties[req.query.key(i)] = prop ;
    props.push(key);
    i = i + 1;

});

I get this:

 [{ props: { a: 'a1' } }, { props: { b: 'b1' } } ]

but in this way I could get only this query:

db.collection.find({"$and": [ { props: { a: 'a1' } }, { props: { b: 'b1' } } ]}

which is completely different from the one I've written above (this one search for a props which is exactly like the ones I've provided, instead the original looks for one which contains one of the values)

how can I do?