how to get type from `cxxNewExpr` in `clang-tidy`

Question

I'm trying to do a quick rewrite of our codebase to replace all instances of new T(...) with New<T>(...) (a custom function), so I can do some local measurements.

I think clang-tidy is the way to go here, so I've made a small clang tidy script, based off of this tutorial I found. The script is able to run, but not pass tests, since I do not match things correctly.

However, I'm running into problems getting the type out of the matched new expression.

What I have so far is:

class ReplaceNewAndDeleteCheck : public utils::TransformerClangTidyCheck {      
 public:                                                                         
   ReplaceNewAndDeleteCheck(StringRef Name, ClangTidyContext *Context)           
      : TransformerClangTidyCheck(MakeRules(), Name, Context) {}                
};     

Where MakeRules is defined as follows:

RewriteRuleWith<std::string> MakeRules() {
  std::string s = "new";
  return makeRule(
    cxxNewExpr().bind(s),
      changeTo(cat("New<", node(s), ">")), 
      cat("")
    );
  }

The script is able to run, but does not give the correct result. For example, with int* x = new int(10);, what I want is int* x = New<int>(10);, but what I get is int* x = New<new int(10)>;.

I know MakeRules is wrong, since I'm binding the entire new expression, not just the on the entire but I can't figure out how to either get the type and arguments out of the new expression, or to bind to those instead.