These problems are from the atcoder DP contest, and were transferred onto DMOJ. All problem statements were made by several atcoder users. As there is no access to the test data, all data is randomly generated. If there are issues with the statement or data, please contact or on slack.
There is a set consisting of positive integers. Taro and Jiro will play the following game against each other.
Initially, we have a pile consisting of stones. The two players perform the following operation alternately, starting from Taro:
- Choose an element in , and remove exactly stones from the pile.
A player loses when he becomes unable to play. Assuming that both players play optimally, determine the winner.
- All values in input are integers.
The first line will contain 2 space separated integers .
The next line will contain space separated integers, .
If Taro will win, print
First; if Jiro will win, print
Sample Input 1
2 4 2 3
Sample Output 1
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
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
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
Sample Input 5
3 21 1 2 3
Sample Output 5
Sample Input 6
1 100000 1
Sample Output 6