Json – Delete all where DOES NOT contain

I have this JSON file json1.json:

{
    "a":"val1",
    "b":"val2",
    "nest1": {
        "z": "x",
        "test": "containval"
    }
}

I need to get a new json where elements whose values that contain val are removed, ANY property can have val, this gets me close:

jq 'del(.. | select(. == "val1"))' .json1.json

it produces this:

{
  "b": "val2",
  "nest1": {
    "z": "x",
    "test": "containval"
  }
}

Except that it checks for values being EQUAL to val1, and I only need where the value DOES NOT CONTAIN "val".

Desired output:

{
    "a":"val1",
    "b":"val2",
    "nest1": {
        "test": "containval"
    }
}