Subtraction Game Oracle
A single pile of n stones; a move removes exactly s stones for some s in the allowed set S; last to move wins. For each query n, print the winner.
Input: the first line has |S| and Q; the second line has the set S; each of the next Q lines has a pile size n.
Output: one line per query: FIRST or SECOND.
Constraints:
- 1 ≤ |S| ≤ 10
- 1 ≤ Q ≤ 104
- 0 ≤ n ≤ 104
- 1 ≤ s ≤ 20
Sample Tests
Input 1
2 3 1 2 0 3 4
Output 1
SECOND SECOND FIRST
Input 2
1 1 2 5
Output 2
SECOND
Discussion (opens after you solve — no spoilers before)
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