planner: refine the codes of embeded limit of double read

cmd/explaintest/r/explain_easy.result

@@ -132,12 +132,11 @@ Projection	10000.00	root		eq(test.t1.c2, test.t2.c2)->Column#11
 └─Apply	10000.00	root		CARTESIAN left outer join
   ├─TableReader(Build)	10000.00	root		data:TableFullScan
   │ └─TableFullScan	10000.00	cop[tikv]	table:t1	keep order:false, stats:pseudo
-  └─Limit(Probe)	10000.00	root		offset:0, count:1
-    └─Projection	10000.00	root		test.t2.c1, test.t2.c2
-      └─IndexLookUp	10000.00	root		
-        ├─Limit(Build)	10000.00	cop[tikv]		offset:0, count:1
-        │ └─IndexRangeScan	10000.00	cop[tikv]	table:t2, index:c1(c1)	range: decided by [eq(test.t1.c1, test.t2.c1)], keep order:true, stats:pseudo
-        └─TableRowIDScan(Probe)	10000.00	cop[tikv]	table:t2	keep order:false, stats:pseudo
+  └─Projection(Probe)	10000.00	root		test.t2.c1, test.t2.c2
+    └─IndexLookUp	10000.00	root		limit embedded(offset:0, count:1)
+      ├─Limit(Build)	10000.00	cop[tikv]		offset:0, count:1
+      │ └─IndexRangeScan	10000.00	cop[tikv]	table:t2, index:c1(c1)	range: decided by [eq(test.t1.c1, test.t2.c1)], keep order:true, stats:pseudo
+      └─TableRowIDScan(Probe)	10000.00	cop[tikv]	table:t2	keep order:false, stats:pseudo
 explain format = 'brief' select * from t1 order by c1 desc limit 1;
 id	estRows	task	access object	operator info
 Limit	1.00	root		offset:0, count:1

planner/core/casetest/testdata/integration_suite_out.json

@@ -14,12 +14,11 @@
       {
         "SQL": "explain format = 'brief' select * from tbl use index(idx_b_c) where b > 1 order by b desc limit 2,1",
         "Plan": [
-          "Limit 1.00 root  offset:2, count:1",
-          "└─Projection 3.00 root  test.tbl.a, test.tbl.b, test.tbl.c",
-          "  └─IndexLookUp 3.00 root  ",
-          "    ├─Limit(Build) 3.00 cop[tikv]  offset:0, count:3",
-          "    │ └─IndexRangeScan 3.00 cop[tikv] table:tbl, index:idx_b_c(b, c) range:(1,+inf], keep order:true, desc",
-          "    └─TableRowIDScan(Probe) 3.00 cop[tikv] table:tbl keep order:false"
+          "Projection 1.00 root  test.tbl.a, test.tbl.b, test.tbl.c",
+          "└─IndexLookUp 1.00 root  limit embedded(offset:2, count:1)",
+          "  ├─Limit(Build) 3.00 cop[tikv]  offset:0, count:3",
+          "  │ └─IndexRangeScan 3.00 cop[tikv] table:tbl, index:idx_b_c(b, c) range:(1,+inf], keep order:true, desc",
+          "  └─TableRowIDScan(Probe) 1.00 cop[tikv] table:tbl keep order:false"
         ]
       },
       {

planner/core/task.go

@@ -897,20 +897,27 @@ func (p *PhysicalLimit) sinkIntoIndexLookUp(t task) bool {
 		}
 	}
 
+	// We can sink Limit into IndexLookUpReader only if tablePlan contains no Selection.
+	ts, isTableScan := reader.tablePlan.(*PhysicalTableScan)
+	if !isTableScan {
+		return false
+	}
+
 	// If this happens, some Projection Operator must be inlined into this Limit. (issues/14428)
 	// For example, if the original plan is `IndexLookUp(col1, col2) -> Limit(col1, col2) -> Project(col1)`,
 	//  then after inlining the Project, it will be `IndexLookUp(col1, col2) -> Limit(col1)` here.
 	// If the Limit is sunk into the IndexLookUp, the IndexLookUp's schema needs to be updated as well,
-	//  but updating it here is not safe, so do not sink Limit into this IndexLookUp in this case now.
+	// So we add an extra projection to solve the problem.
 	if p.Schema().Len() != reader.Schema().Len() {
-		return false
+		extraProj := PhysicalProjection{
+			Exprs: expression.Column2Exprs(p.schema.Columns),
+		}.Init(p.SCtx(), p.statsInfo(), p.blockOffset, nil)
+		extraProj.SetSchema(p.schema)
+		// If the root.p is ready a Projection. We left the optimization for the later Projection Elimination.
+		extraProj.SetChildren(root.p)
+		root.p = extraProj
 	}
 
-	// We can sink Limit into IndexLookUpReader only if tablePlan contains no Selection.
-	ts, isTableScan := reader.tablePlan.(*PhysicalTableScan)
-	if !isTableScan {
-		return false
-	}
 	reader.PushedLimit = &PushedDownLimit{
 		Offset: p.Offset,
 		Count:  p.Count,