Problem:
Score : 100 points

Problem Statement

There is a set A = \{ a_1, a_2, \ldots, a_N \} consisting of N positive integers.
Taro and Jiro will play the following game against each other.

Initially, we have a pile consisting of K stones.
The two players perform the following operation alternately, starting from Taro:

Choose an element x in A, and remove exactly x stones from the pile.

A player loses when he becomes unable to play.
Assuming that both players play optimally, determine the winner.

Constraints

All values in input are integers.

1 \leq N \leq 100

1 \leq K \leq 10^5

1 \leq a_1 < a_2 < \cdots < a_N \leq K

Input

Input is given from Standard Input in the following format:

N K
a_1 a_2 \ldots a_N

Output

If Taro will win, print First; if Jiro will win, print Second.

Sample Input 1

2 4
2 3

Sample Output 1

First

If Taro removes three stones, Jiro cannot make a move.
Thus, Taro wins.

Sample Input 2

2 5
2 3

Sample Output 2

Second

Whatever Taro does in his operation, Jiro wins, as follows:

If Taro removes two stones, Jiro can remove three stones to make Taro unable to make a move.

If Taro removes three stones, Jiro can remove two stones to make Taro unable to make a move.

Sample Input 3

2 7
2 3

Sample Output 3

First

Taro should remove two stones. Then, whatever Jiro does in his operation, Taro wins, as follows:

If Jiro removes two stones, Taro can remove three stones to make Jiro unable to make a move.

If Jiro removes three stones, Taro can remove two stones to make Jiro unable to make a move.

Sample Input 4

3 20
1 2 3

Sample Output 4

Second

Sample Input 5

3 21
1 2 3

Sample Output 5

First

Sample Input 6

1 100000
1

Sample Output 6

Second

Solution in Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)


import java.util.*;

public class Main {

    public static void main(String[] args) {
        Scanner scanner = new Scanner(System.in);
        int n = scanner.nextInt();
        int k = scanner.nextInt();

        HashSet<Integer> items = new LinkedHashSet<>();

        int min = -1;

        for (int i = 0; i < n; i++) {
            int item = scanner.nextInt();
            if (i == 0) min = item;
            items.add(item);
        }

        if (solve(min, items, k, new HashMap<>(), 0) == 0) {
            System.out.println("First");
        } else {
            System.out.println("Second");
        }
    }

    // return winner id 0 means first
    private static int solve(int min, Set<Integer> choices, int k, Map<Integer, Boolean> canWinMemo, int myId) {
        int otherId = 1 - myId;

        if (canWinMemo.containsKey(k)) return canWinMemo.get(k) ? myId : otherId;

        if (k < min) return otherId;
        if (choices.contains(k)) return myId;

        int winnerId = otherId;

        for (int choice : choices) {
            if (choice > k) break;
            if (solve(min, choices, k - choice, canWinMemo, otherId) == myId) {
                winnerId = myId;
                break;
            }
        }
        canWinMemo.put(k, winnerId == myId);
        return winnerId;
    }
}