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Alice and Bob are playing a game on a graph. They have an undirected graph without self-loops and multiple edges. All vertices of the graph have degree equal to $$$2$$$. The graph may consist of several components. Note that if such graph has $$$n$$$ vertices, it will have exactly $$$n$$$ edges.
Alice and Bob take turn. Alice goes first. In each turn, the player can choose $$$k$$$ ($$$l \le k \le r$$$; $$$l < r$$$) vertices that form a connected subgraph and erase these vertices from the graph, including all incident edges.
The player who can't make a step loses.
For example, suppose they are playing on the given graph with given $$$l = 2$$$ and $$$r = 3$$$:
A valid vertex set for Alice to choose at the first move is one of the following:
Then a valid vertex set for Bob to choose at the first move is one of the following:
Alice can't make a move, so she loses.
You are given a graph of size $$$n$$$ and integers $$$l$$$ and $$$r$$$. Who will win if both Alice and Bob play optimally.
The first line contains three integers $$$n$$$, $$$l$$$ and $$$r$$$ ($$$3 \le n \le 2 \cdot 10^5$$$; $$$1 \le l < r \le n$$$) — the number of vertices in the graph, and the constraints on the number of vertices Alice or Bob can choose in one move.
Next $$$n$$$ lines contains edges of the graph: one edge per line. The $$$i$$$-th line contains two integers $$$u_i$$$ and $$$v_i$$$ ($$$1 \le u_i, v_i \le n$$$; $$$u_i \neq v_i$$$) — description of the $$$i$$$-th edge.
It's guaranteed that the degree of each vertex of the given graph is equal to $$$2$$$.
Print Alice (case-insensitive) if Alice wins, or Bob otherwise.
6 2 3 1 2 2 3 3 1 4 5 5 6 6 4
Bob
6 1 2 1 2 2 3 3 1 4 5 5 6 6 4
Bob
12 1 3 1 2 2 3 3 1 4 5 5 6 6 7 7 4 8 9 9 10 10 11 11 12 12 8
Alice
In the first test the same input as in legend is shown.
In the second test the same graph as in legend is shown, but with $$$l = 1$$$ and $$$r = 2$$$.
Informação
Provedor Codeforces
Código CF1823E
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Datas 09/05/2023 10:39:01
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