Need to merge jsons representing parent child relationship

Question

I have json values to be depicted in jstree format I want a union of json1 and json2 like the following merged json

The data for this jstree is in the following format json1:

[
       { "id" : "ajson2", "parent" : "#", "text" : "Root node 2" },
       { "id" : "ajson3", "parent" : "ajson2", "text" : "Child 1" },
       { "id" : "ajson4", "parent" : "ajson2", "text" : "xxxxx" },
    ]

json2:

[
       { "id" : "ajson2", "parent" : "#", "text" : "Root node 2" },
       { "id" : "ajson3", "parent" : "ajson2", "text" : "Child 1" },
       { "id" : "ajson4", "parent" : "ajson2", "text" : "yyyyy" },
    ]

Desired output:

[
       { "id" : "tree1ajson2", "parent" : "#", "text" : "Root node 2" },
       { "id" : "tree1ajson3", "parent" : "tree1ajson2", "text" : "Child 1" },
       { "id" : "tree1ajson4", "parent" :"tree1ajson2", "text" : "xxxxx", "supportedTree":"tree1"},
       { "id" : "tree2ajson4", "parent" : "tree1ajson2", "text" : "yyyyy", "supportedTree":"tree2" },
    ]

Conditions:

1. A parent can have any depth of descendants
2. In case, a folder is present only on one tree, itself and all its descendants should be added to mergedtree with the "supportedTree" key and value.
3. ids can overlap. Eg: xxxxx and yyyyy have the id ajson4 in our example