PROBLEM DESCRIPTION

Given $3$ positive integers, $n$, $b$, and $s$, generate the next $n$ numbers in base $b$ starting with $s$ in the given base. We guarantee that the base will be between $2$ and $16$ inclusive. We guarantee that $s$ is a valid number in base $b$. Find all of the digits in the numbers generated and print the number of times, in base $10$, that the most frequently found digit occurs.

INPUT FORMAT

There will be three values representing how many numbers to generate, the base to be used between $2$ and $16$ inclusive, and the starting value in the base given that will be no more than $16$ digits long. We guarantee that $s$ is a valid number in base $b$.

OUTPUT FORMAT

For each set of $3$ input values, find how many times each digit occurs in the sequence of numbers generated. Then output the number of times the digit that is found the most actually occurs.

SAMPLE

INPUT #1

15 8 2

OUTPUT #1

9

INPUT #2

25 2 1111011

OUTPUT #2

105

INPUT #3

20 12 9AB

OUTPUT #3

14

INPUT #4

10 16 ABCDEF

OUTPUT #4

10

INPUT #5

1000 2 1

OUTPUT #5

4938

EXPLANATION

Sample #1 Explanation

If $n=15$, $b=8$, and $s=2$, the numbers generated are $2, 3, 4, 5, 6, 7, 10, 11, 12, 13, 14, 15, 16, 17, 20$. The digit that occurs most frequently is $1$ which occurs $9$ times so the output would be $9$.