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++14 (GCC 5.4.1) (judge verdict: Accepted)


#include <iostream>
#include <cstdio>
#include <vector>
#include <cmath>
#include <map>
#include <set>
#include <algorithm>
#include <string>
#include <queue>
#define PIE 3.14159265358979
#define rep(i,n) for(int i = 0;i < (n);i++)
using namespace std;
typedef long long ll;

bool dp[100005]; //0:Secondの勝ち

int main(){
    int N,K;
    int a[100];
    cin>>N>>K;
    for(int i  = 0;i < N;i++){
        cin>>a[i];
    }
    for(int i  = 0;i < K;i++){
        bool next_win = 0;
        if(dp[i]==0)
            next_win = 1;
        for(int j  = 0;j < N;j++){
            int next_k = i+a[j];
            if(next_k>K){
                continue;
            }
            if(dp[next_k]==0&&next_win==1){
                dp[next_k]=1;
            }
        }
    }
    
    if(dp[K]==1){
        cout<<"First"<<endl;
    }else{
        cout<<"Second"<<endl;
    }

}