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.Scanner;

public class Main {
    public static void main(String[] args) {
        Scanner scanner = new Scanner(System.in);
        int n = scanner.nextInt();
        int k = scanner.nextInt();
        int[] as = new int[n];
        Boolean[][] fdp = new Boolean[k + 1][2];
        fdp[0][0] = false;
        fdp[0][1] = false;
        for (int i = 0; i < n; i++) {
            as[i] = scanner.nextInt();
        }
        for (int i = 0; i < as[0]; i++) {
            fdp[i][1] = false;
        }
        System.out.println(calculate(fdp, as, k, 0) ? "First" : "Second");
    }

    private static boolean calculate(Boolean[][] fdp, int[] as, int k, int order) {
        if (fdp[k][order] != null) {
            return fdp[k][order];
        }
        fdp[k][order] = false;
        for (int i = 0; i < as.length; i++) {
            if (k - as[i] >= 0) {
                fdp[k][order] |= !calculate(fdp, as, k - as[i], (order + 1) % 2);
              	if (fdp[k][order]) {
                    break;
                }
            }
        }
        return fdp[k][order];
    }
}