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