Canadian Computing Competition: 2025 Stage 1, Senior #2

Cyrene, the captain of the Cryptogram Cracking Club (CCC), came across a concerningly long cipher. Conveniently, this cipher is composed of lower-case characters ( a-z ). Comfortingly, the cipher is composed of a pattern that repeats infinitely.

Cyrene wishes to locate the \(c\) -th character of the cipher. To make your job easier, the CCC members have extracted the repeated pattern and compressed it using the Run-Length Encoding (RLE) algorithm, which replaces consecutive repeated characters with a single occurrence of the character followed by a count of how many times it was repeated. For example, for the pattern aaaabccdddd , the RLE algorithm outputs a4b1c2d4 .

You are given the output of the RLE algorithm for a certain pattern. Can you determine the \(c\) -th character of the long cipher that is formed by repeating this pattern infinitely?

Input Specification

The first line of input will consist of a string \(S\) , representing a pattern produced by the RLE algorithm. The length of \(S\) will be at least \(2\) and at most \(2 \cdot 10^5\) . Additionally, all numbers appearing in \(S\) are between \(1\) and \(10^{12}\) .

The next line of input contains a single integer \(c\) , representing the index of the character you wish to locate, starting from index \(0\) .

The following table shows how the available \(15\) marks are distributed:

Output Specification

Output the \(c\) -th character of the long cipher.

Sample Input 1

r2d2
8

Sample Output 1

r

Explanation for Sample Output 1

The output of the RLE algorithm r2d2 corresponds to the pattern rrdd , which creates the infinitely long cipher rrddrrddrrddrrdd... , where the \(c = 8\) th character is r . In this example, the \(c = 8\) th character is highlighted with a box around it.

Sample Input 2

a4b1c2d10
100

Sample Output 2

d

Explanation for Sample Output 2

The output of the RLE algorithm a4b1c2d10 corresponds to the pattern aaaabccdddddddddd . When repeated infinitely, the \(c = 100\) th character is d .