21489_CoinGame

After hh has learned how to play Nim game, he begins to try another coin game which seems much easier.

The game goes like this:

Two players start the game with a circle of N coins.

They take coins from the circle in turn and every time they could take 1~K continuous coins.

(imagining that ten coins numbered from 1 to 10 and K equal to 3, since 1 and 10 are continuous, you could take away the continuous 10, 1, 2, but if 2 was taken away, you couldn't take 1, 3, 4, because 1 and 3 aren't continuous)

The player who takes the last coin wins the game.

Suppose that those two players always take the best moves and never make mistakes.

Your job is to find out who will definitely win the game.

The first line is a number T ( 1 ≤ T ≤ 100 ), represents the number of case. The next T blocks follow each indicates a case.

Each case contains two integers N ( 3 ≤ N ≤ 10⁹, 1 ≤ K ≤ 10 ).

For each case, output the number of case and the winner "first" or "second". (as shown in the sample output)

2
3 1
3 2

Case 1: first
Case 2: second