Max factor of the permutations of a list

gistfile1.scala

object permutations {
	def insertAt[T](e: T, p: Int, l: List[T]): List[T] = p match {
		case 0 => e :: l
		case _ => l.head :: insertAt(e, p-1, l.tail)
	}                                         //> insertAt: [T](e: T, p: Int, l: List[T])List[T]

	def permute[T] (l: List[T]): List[List[T]] = l match {
		case Nil => Nil
		case h :: t =>
			println(h, t)
			permute(t) match {
				case Nil => List(List(h))
				case permutations =>
				for {
					permutation <- permutations
					i <- 0 to permutation.length
				} yield insertAt(h, i, permutation)
			}
	}                                         //> permute: [T](l: List[T])List[List[T]]
	
	def factor (a: List[Int], b: List[Int]): Int = {
		if (a.length == 0 || b.length == 0) 0
		else {
			val ah = a.head
			val bh = b.head
		
			(ah*bh) + factor (a.tail, b.tail)
		}
	}                                         //> factor: (a: List[Int], b: List[Int])Int
	
	def maxFactor (a: List[List[Int]], b: List[List[Int]], max: Int = 0): Int = {
		if (a.length == 0 || b.length == 0) {max}
		else {
			val al = a.head
			val bl = b.head
			maxFactor(a.tail, b.tail, math.max(max, factor(al, bl)))
		}
	}                                         //> maxFactor: (a: List[List[Int]], b: List[List[Int]], max: Int)Int
	
	val a = permute (List(1,2,3))             //> (1,List(2, 3))
                                                  //| (2,List(3))
                                                  //| (3,List())
                                                  //| a  : List[List[Int]] = List(List(1, 2, 3), List(2, 1, 3), List(2, 3, 1), Lis
                                                  //| t(1, 3, 2), List(3, 1, 2), List(3, 2, 1))
	val b = permute (List(4,5,6))             //> (4,List(5, 6))
                                                  //| (5,List(6))
                                                  //| (6,List())
                                                  //| b  : List[List[Int]] = List(List(4, 5, 6), List(5, 4, 6), List(5, 6, 4), Lis
                                                  //| t(4, 6, 5), List(6, 4, 5), List(6, 5, 4))
	
	maxFactor (a,b)                           //> res0: Int = 32
   
}