Byteman keeps all of his savings in an old safe. The lock of this safe consists of $ n $ identical wheels, each of them has the same word consisting of $ m $ letters written on it. Wheels can be rotated independently of each other (this way each wheel can be put in $ m $ different positions). Safe gets opened, when for all $ m $ positions letters written on all wheels for that position are the same.
Recently one of the Byteman's acquaintance told him that it is a good idea to keep money in a bank. Byteman decided to open his safe as soon as possible and transfer all of his money to a high-interest bank account. Assuming that rotation of any wheel by $\frac{360}{m}$ degrees to the left or to the right can be performed within one second, calculate, how long would it take (at minimum) to open Byteman's safe.
Help Byteman!
Input Format
The first line of the standard input contains two integers $ n $ and $ m $ ($2 ≤ n, m ≤ 1\,000\,000$), separated with a single space and denoting the number of wheels in the lock and the length of the word written on each wheel. The second line of the input contains one word $s_1s_2\ldots s_m$ of length $ m $, consisting of large English letters. In the third line there are $ n $ integers $o_1o_2\ldots o_n$ ($0 ≤ o_{i} < m $), separated with single spaces. $ o_{i} = k $ means that the word from the $ i $'th wheel is rotated by $ k $ positions to the left (relatively to some defined initial position), which means it is set in position $ s_{k+1}s_{k+2} \ldots s_{m}s_{1}s_{2}\ldots s_{k} $. For instance, if $ o_{i} = 0$ then the word on the $ i $'th wheel is not rotated at all.
Output Format
The first and only line of the standard output should contain one integer, the minimal time required to open Byteman's safe.
Example
Input
4 6 SLOWIK 2 0 3 5
Output
6
Notes
For the example lock, words written on each wheel look as follows:
OWIKSL SLOWIK WIKSLO KSLOWI
For example, rotating the first wheel by one position to the left gives WIKSLO. When we rotate the same wheel to the right instead, we get LOWIKS.