Max loves balanced bracket sequences, and things that are deep. Thus, he decided to put the two together and create a deep bracket sequence. Unfortunately for him, the balanced bracket sequence he was given for his birthday is not very deep. Can you help him make it deeper? We define a flip to be an operation where you change a ( to a ) or vice versa. Max wants you to demonstrate the minimum number of flips he must execute to make his bracket sequence have depth at least ~K~. Note that the sequence may become unbalanced after the intermediate flips.

A bracket sequence is balanced if you can match every open bracket ( with a closed bracket ) that comes later in the sequence.

We define the depth of a bracket sequence to be the maximum number of nested bracket pairs. For example, the sequence ((()(()))) has depth ~4~ because ((()(()))) is ~4~ nested bracket pairs, and you cannot nest more than ~4~.

Input Specification

The first line of input contains an integer ~N\ (1 \leq N \leq 2\cdot 10^5)~, ~N~ is even, and ~K\ (1 \leq K \leq \frac{N}{2})~.

The next line of input contains a balanced bracket sequence of length ~N~.

Output Specification

On one line, you are to output ~F~: the minimum number of flips you must make for the balanced bracket sequence to have depth at least ~K~.

On the next line, you are to output ~F~ integers, the ~i^\text{th}~ integer being the ~i^\text{th}~ bracket you flip. If there are multiple solutions, you are to print the lexicographically least. If ~F=0~, this line is blank (still print a line though).

Subtask 1 (10%)

~N \leq 20~

Subtask 2 (90%)

No further constraints.

Sample Input

10 5
((()))()()

Sample Output

4
4 5 7 9