如何对MongoDB聚合进行分组

Question

下面是我在MongoDB集合中拥有的数据。

{ "_id" : ObjectId("758452161603f94848510101"), "exam_date" : ISODate("2020-01-01T00:00:00Z") "passed" : 1 }
{ "_id" : ObjectId("758452161603f94848510102"), "exam_date" : ISODate("2020-01-22T00:00:00Z") "passed" : 0 }
{ "_id" : ObjectId("758452161603f94848510103"), "exam_date" : ISODate("2020-01-28T00:00:00Z") "passed" : 0 }
{ "_id" : ObjectId("758452161603f94848510204"), "exam_date" : ISODate("2020-02-01T00:00:00Z") "passed" : 1 }
{ "_id" : ObjectId("758452161603f94848510205"), "exam_date" : ISODate("2020-02-02T00:00:00Z") "passed" : 0 }
{ "_id" : ObjectId("758452161603f94848510206"), "exam_date" : ISODate("2020-02-03T00:00:00Z") "passed" : 1 }
{ "_id" : ObjectId("758452161603f94848510207"), "exam_date" : ISODate("2020-02-04T00:00:00Z") "passed" : 1 }

下面是我正在做的汇总，但是预计会有不同的输出。

db.students.aggregate([
    {$group: {
        _id: {$substr: ['$exam_date', 5, 2]}, 
        totalStudents: {$sum: 1}
    }}
]);

实际输出：

    { "_id" : "01", "totalStudents" : 3 }
    { "_id" : "02", "totalStudents" : 4 }

预期输出：

    { "_id" : "01", "totalStudents" : 3, "passed" : 1, "failed" : 2}
    { "_id" : "02", "totalStudents" : 4, "passed" : 3, "failed" : 1}