Dice Roller

Create a Dice class that simulates rolling a die. The constructor takes the number of sides and a seed. Add a roll() method that returns the next result using java.util.Random.

Important: Create the Random object with new Random(seed) and use nextInt(sides) + 1 so results are reproducible for a given seed.

Read the number of sides, the seed, and the number of rolls from stdin. Create a Dice object and print each roll result on a separate line.

Input

• Line 1: the number of sides (integer, at least 1; any positive int value)
• Line 2: seed (integer, any int value)
• Line 3: the number of rolls (integer, 0 <= rolls <= 2·10^4)

Output

• One line per roll with the result (an integer between 1 and sides).

Examples

Input:
6
42
1

Output:
3

Input:
6
1
3

Output:
4
5
2

Input:
20
7
1

Output:
17

Input:
2
100
5

Output:
2
2
1
2
2

Different seeds (and different sides) produce completely different sequences, but the same seed always reproduces the same sequence.