Round Sugoroku

Aoi of JOI High School bought a new sugoroku board. The board consists of N+2 squares in a single horizontal row. The squares are numbered from 0 to N+1 in order from the leftmost square to the rightmost square. Initially, squares 0 and N+1 have X written on them, and square i (1 ≦ i ≦ N) has Si written on it. Here, Si is either the character . or #.

Aoi is playing with this board and one piece. Initially, the piece is placed on square A (1 ≦ A ≦ N) facing right. Here, SA is the character .. Every second, Aoi moves the piece one square in the direction it is facing.

The board has the following rules.

• When the piece lands on a square with X, the direction of the piece is reversed.
• When the piece lands on a square with ., nothing happens.
• When the piece lands on a square with #, the direction of the piece is reversed. At this time, the character written on this square is changed to .. Therefore, after that, even if the piece lands on this square, the direction is not reversed.

The time needed to reverse the piece or change a character can be ignored.

Given the initial state of the board and the piece, write a program to find the time required until all squares with # disappear.

The input is given from standard input in the following format.

N A
S

Here, S is a string of length N, and its i-th character (1 ≦ i ≦ N) is Si.

Print in one line to standard output the number of seconds required until all squares with # disappear.

• 2 ≦ N ≦ 200 000.
• 1 ≦ A ≦ N.
• Si is either the character . or # (1 ≦ i ≦ N).
• SA is the character ..
• There is at least 1 index i (1 ≦ i ≦ N) such that Si is the character #.