Lemurian parties#11120
Lemur King Julian has exactly lemurs under his control, lemurs of each of species. Julian loves to party, so every night he throws a party, but unfortunately the VIP area only has enough seats for him and other lemurs.
Since Julian does not like to have "identical" parties, every day he must choose whom to invite to the VIP area so that the sets of lemurs in the VIP area never repeat. Two lemurs of the same species are considered indistinguishable. Sets are considered the same if they match as multisets of lemur species.
Help Julian determine how many days he can organize different parties. Since the answer can be large, print it modulo .
The only line contains three integers , , and (1 \le k \le 500\;000, 0 \le n \le 2k, 2 \le m \le 10^9) — the number of lemur species, the number of seats in the VIP area, and the modulo to print the answer.
Print one integer — the answer to the problem modulo .
Example 1
Example 2