K. Addition Robot
time limit per test
3 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

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

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.
Output

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

Example
Input
5 3
ABAAA
2 1 5 1 1
1 3 5
2 2 5 0 1000000000
Output
11 3
0 1000000000
Note

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 $$$(0, 1\,000\,000\,000)$$$.