In a tournament, there are n teams $$T_1, T_2, ..... T_n$$, with n > 5. Each team consists of k players, k > 3. The following pairs of teams have one player in common $$T_1, T_2$$ and $$T_3, T_{n-1}$$ and $$T_n$$ and $$T_1$$ No other pair of teams has any player in common. How many players are participating in the tournament, considering all the n team together?

A

k (n-1)

B

n (k-2)

C

k (n-2)

D

n (k-1)