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 C (GCC 5.4.1) (judge verdict: Accepted)

#include <stdio.h>
#include <stdlib.h>

int calculate_dp(int *DP, int k, int *a, int N) {
    if (DP[k] != 0)
        return DP[k];
    for (int i = N; i >= 1; i--) {
        if (k >= a[i]) {
            if (calculate_dp(DP, k - a[i], a, N) == 1) {
                //printf("相手が負ける選び方(k:%d, a[%d]): %d:", k, i, a[i]);
                return DP[k] = 2;
            }
        }
    }
    return DP[k] = 1;
}

int main () {
    int N;
    int K;
    scanf("%d", &N);
    scanf("%d", &K);

    int *a = malloc((N + 1) * sizeof(int));
    int *DP = calloc(K + 1, sizeof(int));
    for (int i = 1; i <= N; i++) {
        scanf("%d", &a[i]);
    }

    calculate_dp(DP, K, a, N);

    if (DP[K] == 2)
        printf("%s\n", "First");
    else
        printf("%s\n", "Second");

    return 0;
}