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.

Explanation

Example:

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 frequencies are:

• Digit 1 occurs 9 times.
• Digits 0, 2, 3, 4, 5, 6, 7 each occur 2 times.

The digit that occurs most frequently is 1, which occurs 9 times, so the output would be 9.

Sample Input / Output

15 8 2

9

25 2 1111011

105

20 12 9AB

14

10 16 ABCDEF

10

1000 2 1

4938