E. Removing Graphtime limit per test2 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputAlice 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:   \{1, 2\}  \{1, 3\}  \{2, 3\}  \{4, 5\}  \{4, 6\}  \{5, 6\}  \{1, 2, 3\}  \{4, 5, 6\}  Suppose, Alice chooses subgraph \{4, 6\}.Then a valid vertex set for Bob to choose at the first move is one of the following:   \{1, 2\}  \{1, 3\}  \{2, 3\}  \{1, 2, 3\}  Suppose, Bob chooses subgraph \{1, 2, 3\}.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.InputThe 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.OutputPrint Alice (case-insensitive) if Alice wins, or Bob otherwise.ExamplesInput
6 2 3
1 2
2 3
3 1
4 5
5 6
6 4
Output
Bob
Input
6 1 2
1 2
2 3
3 1
4 5
5 6
6 4
Output
Bob
Input
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
Output
Alice
NoteIn 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.
6 2 3
1 2
2 3
3 1
4 5
5 6
6 4

Bob 
['brute force', 'dp', 'games', 'graphs', 'math', '*2500']