Lemurian parties - easy#11269
King Julien, the ruler of all lemurs, has exactly 2 \cdot k lemurs under his command — two lemurs of each of the species. Julien loves parties, so every evening he throws one. However, the VIP area unfortunately has room only for himself and other lemurs.
Since Julien dislikes repeating himself, he wants to invite a set of lemurs to the VIP area that has never appeared before. Two lemurs of the same species are considered indistinguishable. Two sets of lemurs are considered the same if they coincide as multisets of species.
Help Julien determine how many distinct parties he can host. As the answer may be very large, print it modulo 10^9 + 7.
A single line contains two integers and n~(1 \le k \le 500000,~0 \le n \le 2 \cdot k) — the number of lemur species and the number of available VIP seats (excluding Julien himself).
Print one single integer — the number of distinct parties modulo 10^9 + 7.
Example 1
Example 2