Wrap Around

题意翻译

给定一个字符串 $s$，字符集为 $\{0,1\}$。 求有多少长度为 $n$ 的字符串 $t$，满足以 $t$ 为循环节的无限循环字符串包含 $s$。 $1\le|s|\le n\le 40$

题目描述

You are given a binary string $ s $ . Find the number of distinct cyclical binary strings of length $ n $ which contain $ s $ as a substring. The cyclical string $ t $ contains $ s $ as a substring if there is some cyclical shift of string $ t $ , such that $ s $ is a substring of this cyclical shift of $ t $ . For example, the cyclical string "000111" contains substrings "001", "01110" and "10", but doesn't contain "0110" and "10110". Two cyclical strings are called different if they differ from each other as strings. For example, two different strings, which differ from each other by a cyclical shift, are still considered different cyclical strings.

输入输出格式

输入格式

The first line contains a single integer $ n $ ( $ 1 \le n \le 40 $ ) — the length of the target string $ t $ . The next line contains the string $ s $ ( $ 1 \le |s| \le n $ ) — the string which must be a substring of cyclical string $ t $ . String $ s $ contains only characters '0' and '1'.

输出格式

Print the only integer — the number of distinct cyclical binary strings $ t $ , which contain $ s $ as a substring.

输入输出样例

输入样例 #1

2
0

输出样例 #1

3

输入样例 #2

4
1010

输出样例 #2

2

输入样例 #3

20
10101010101010

输出样例 #3

962

说明

In the first example, there are three cyclical strings, which contain "0" — "00", "01" and "10". In the second example, there are only two such strings — "1010", "0101".