nouns

In the sentence:

The two methods require two different kinds of prior information

a colleague of mine suggests that it should be "kind of" instead.

I was quite certain that the first form was correct, but reading various online sources on singular vs. plural use in relation to "kind of" has got me confused. Still, it seems to me that the examples where it is a bit ambiguous are those where the quantity is implied by how you interpret the sentence. In the current case, I still lean towards "two kinds" because it seems it is explicitly "kind" there are two of. Which one is right?

NB: I am not a native English speaker.