Select documents in collection that match foreign key value

Question

I want to use MongoDB aggregate to grab some documents in collection Events that reference the collection Program with the constraint of Program.type

Events

{
   _id: ObjectId,
   programId: ObjectId
}

Programs

{
   _id: ObjectId,
   type: "Type A"
}

The pseudo sql-like query would be like select * from events where event.id = 1234 and where program.type = "Type A"

I've got this and I have no idea what I'm doing.

const pipeline = [
  {
    $match: {_id: id}
  },
  {
    $lookup: {
        from: 'programs',
        localField: '_id',
        foreignField: 'programId',
        as: 'program'
    }
  },
  {
    $unwind: '$program'
  },
  {
    $match: {'program.type': 'Type A'}
  }
]

I actually thought this worked but it failed when I tried different types.