Educational DP Contest AtCoder K - Stones

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Points: 10
Time limit: 1.0s
Memory limit: 1G

Problem types

There is a set A = \{a_1, a_2, \dots, 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 \le N \le 100
  • 1 \le K \le 10^5
  • 1 \le a_1 < a_2 < \dots < a_N \le K

Input Specification

The first line will contain 2 space separated integers N, K.

The next line will contain N space separated integers, a_1, a_2, \dots, a_N.

Output Specification

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

Sample Input 1

2 4
2 3

Sample Output 1

First

Explanation For Sample 1

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

Sample Input 2

2 5
2 3

Sample Output 2

Second

Explanation For Sample 2

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

Explanation For Sample 3

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

Comments


  • 0
    GrenZend  commented on Jan. 14, 2022, 6:08 p.m. edited

    Guys, don't be like me, take your time and don't spam code. :) my bug was so silly lol.


    • 0
      Spitfire720  commented on Jan. 14, 2022, 6:11 p.m.

      You heard the man