Codeforces Round 554 (Div. 2) |
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Finished |
This problem is same as the next one, but has smaller constraints.
Aki is playing a new video game. In the video game, he will control Neko, the giant cat, to fly between planets in the Catniverse.
There are $$$n$$$ planets in the Catniverse, numbered from $$$1$$$ to $$$n$$$. At the beginning of the game, Aki chooses the planet where Neko is initially located. Then Aki performs $$$k - 1$$$ moves, where in each move Neko is moved from the current planet $$$x$$$ to some other planet $$$y$$$ such that:
This way, Neko will visit exactly $$$k$$$ different planets. Two ways of visiting planets are called different if there is some index $$$i$$$ such that the $$$i$$$-th planet visited in the first way is different from the $$$i$$$-th planet visited in the second way.
What is the total number of ways to visit $$$k$$$ planets this way? Since the answer can be quite large, print it modulo $$$10^9 + 7$$$.
The only line contains three integers $$$n$$$, $$$k$$$ and $$$m$$$ ($$$1 \le n \le 10^5$$$, $$$1 \le k \le \min(n, 12)$$$, $$$1 \le m \le 4$$$) — the number of planets in the Catniverse, the number of planets Neko needs to visit and the said constant $$$m$$$.
Print exactly one integer — the number of different ways Neko can visit exactly $$$k$$$ planets. Since the answer can be quite large, print it modulo $$$10^9 + 7$$$.
3 3 1
4
4 2 1
9
5 5 4
120
100 1 2
100
In the first example, there are $$$4$$$ ways Neko can visit all the planets:
In the second example, there are $$$9$$$ ways Neko can visit exactly $$$2$$$ planets:
In the third example, with $$$m = 4$$$, Neko can visit all the planets in any order, so there are $$$5! = 120$$$ ways Neko can visit all the planets.
In the fourth example, Neko only visit exactly $$$1$$$ planet (which is also the planet he initially located), and there are $$$100$$$ ways to choose the starting planet for Neko.
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