Missing Word (APCS 2024-06 Advanced)

2.0s 256M

Given a sorted alphabet \(A\) of distinct lowercase letters, a length \(L\), and a lowercase string \(S\), find the lexicographically smallest length-\(L\) word over \(A\) that is not a substring of \(S\). Letters may repeat. An answer exists. \(S\) may contain letters outside \(A\).

Input

Three lines contain \(A\), \(L\), and \(S\).

Constraints

\(1\le|A|\le10\), \(1\le L\le8\), \(|A|^L\le600000\), \(L\le|S|\le500000\).

Output

Print the smallest missing word.

Scoring

Each scored test independently awards 5 points, totaling 100. Samples award no points.

  • 1: 20% — \(|S|=1000\)
  • 2: 80% — No additional restrictions.

Sample Input 1

acm
2
accaamcm

Sample Output 1

ma

Sample Input 2

dp
3
dddppdpd

Sample Output 2

pdd

Source

o078 · 2024-06 APCS.

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