A13008 | 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: ```
<pre class="lstlisting">```
function f(L, R, A, B):<br></br> FOR i from L to R<br></br> if S[i] = 'A'<br></br> A = A + B<br></br> else<br></br> B = A + B<br></br> return (A, B)<br></br>
```
```

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 $1\,000\,000\,007$ .