AWS API Gateway Mapping Template to add all header, query, path, and stage parameters to JSON dynamically

gistfile1.txt

{
    "request": {
        "context": {
            "stage": "$context.stage"
        },
        "path": {
        #foreach( $key in $input.params().path.keySet())
            "$key": "$input.params().path.get($key)"#if( $velocityHasNext ),#end
        #end
        },
        "headers": {
        #foreach( $key in $input.params().header.keySet())
            "$key": "$input.params().header.get($key)"#if( $velocityHasNext ),#end
        #end
        },
        "query": {
        #foreach( $key in $input.params().querystring.keySet())
            "$key": "$input.params().querystring.get($key)"#if( $velocityHasNext ),#end
        #end
        },
        "stage": {
        #foreach( $key in $stageVariables.keySet())
            "$key": "$stageVariables.get($key)"#if( $velocityHasNext ),#end
        #end
        },
        "body": $input.json('$')
    }
}