40. In the school, there are 400 students, among them 200 are underachievers and 200 are top students. For New Year, Santa Claus brought a bag containing 800 "Almond Ivanovich" candies. He wants to distribute all the candies to the children, with each underachiever receiving no more than one candy, and each top student receiving at least 2 candies, and an even number of them. The school principal decided to reward the top students by preparing 600 tangerines, which he wants to distribute so that each top student receives at least one. Who has more ways to distribute their gifts, and by how many times?
$\square$ Answer: the number of ways is the same.

Let's establish a one-to-one correspondence. Suppose each excellent student takes sponsorship over one of the poor students (different excellent students over different poor students). If the principal gives $2 k+1$ tangerines to a certain excellent student, Santa Claus can give him $2 k+2$ candies, and 0 candies to his sponsored student. If the principal gives the excellent student $2 k$ tangerines, let Santa Claus give 1 candy to his sponsored student, and $2 k$ candies to him.

(folklore)