CF1252K.Addition Robot

Adding two numbers several times is a time-consuming task, so you want to build a robot. The robot should have a string $S = S_1 S_2 \dots S_N$ of $N$ characters on its memory that represents addition instructions. Each character of the string, $S_i$ , is either 'A' or 'B'.

You want to be able to give $Q$ commands to the robot, each command is either of the following types:

• 1 $L$ $R$ . The robot should toggle all the characters of $S_i$ where $L \le i \le R$ . Toggling a character means changing it to 'A' if it was previously 'B', or changing it to 'B' if it was previously 'A'.
• 2 $L$ $R$ $A$ $B$ . The robot should call $f(L, R, A, B)$ and return two integers as defined in the following pseudocode: ```

  ```
      function f(L, R, A, B):
  
        FOR i from L to R
  
          if S[i] = 'A'
  
            A = A + B
  
          else
  
            B = A + B
  
        return (A, B)
  
  
  ```
  ```
  

You want to implement the robot's expected behavior.

Input begins with a line containing two integers: $N$ $Q$ ( $1 \le N, Q \le 100\,000$ ) representing the number of characters in the robot's memory and the number of commands, respectively. The next line contains a string $S$ containing $N$ characters (each either 'A' or 'B') representing the initial string in the robot's memory. The next $Q$ lines each contains a command of the following types.

• 1 $L$ $R$ ( $1 \le L \le R \le N$ )
• 2 $L$ $R$ $A$ $B$ ( $1 \le L \le R \le N$ ; $0 \le A, B \le 10^9$ )

There is at least one command of the second type.

For each command of the second type in the same order as input, output in a line two integers (separated by a single space), the value of $A$ and $B$ returned by $f(L, R, A, B)$ , respectively. As this output can be large, you need to modulo the output by $1\,000\,000\,007$ .

Explanation for the sample input/output #1

For the first command, calling $f(L, R, A, B)$ causes the following:

• Initially, $A = 1$ and $B = 1$ .
• At the end of $i = 1$ , $A = 2$ and $B = 1$ .
• At the end of $i = 2$ , $A = 2$ and $B = 3$ .
• At the end of $i = 3$ , $A = 5$ and $B = 3$ .
• At the end of $i = 4$ , $A = 8$ and $B = 3$ .
• At the end of $i = 5$ , $A = 11$ and $B = 3$ .

Therefore, $f(L, R, A, B)$ will return $(11, 3)$ .For the second command, string $S$ will be updated to "ABBBB".

For the third command, the value of $A$ will always be $0$ and the value of $B$ will always be $1\,000\,000\,000$ . Therefore, $f(L, R, A, B)$ will return $(0, 1\,000\,000\,000)$ .