Molting

A new species of snake found in the Seaburi Plateau is characterized by a pattern of circles (o's) and crosses (x's) arranged in a row from head to tail. The pattern varies from individual to individual, as illustrated below.

xxoooxxxoox

When the snake molts, it grows by stretching all the way across the area between the two circles. The new area will have a pattern of circles, crosses, and circles.

For example, if a snake ooo with a length of 3 molts once, it will have a pattern of circles, crosses, and circles between the first and second and second and third circles from the left, so the molted snake will look like ooxoooxoo . After one more molt, the snake becomes ooxoooxoooxooxooxooxoo and its length becomes 21.

You are studying the ecology of this snake, and you are concerned that if this snake continues to molt, it may grow to a tremendous length.

Given the pattern of the snake and the number of times it has molted, write a program to find the length of the snake after it has molted this times.

Input

The input is given in the following form.

$L$ $N$
$snake$

In the first line, the length of the snake before molting $L$ ($1 \leq L \leq 100$), and the number of times it has molted $N$ ($1 \leq N \leq 50$) are given. The next line contains a string $snake$ of length $L$ which represents the pattern of the snake before it molts. $snake$ is composed of lowercase letters x and o.

Output

Output the length of the snake on a line.

Sample Input and Output

Sample Input 1

3 2
ooo

Sample Output 1

21

Sample Input 2

3 4
xoo

Sample Output 2

48

Sample Input 3

13 30
xooxoooxxxoox

Sample Output 3

12884901889

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