K. Addition Robottime limit per test3 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputAdding 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.InputInput 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.OutputFor 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.ExampleInput
5 3
ABAAA
2 1 5 1 1
1 3 5
2 2 5 0 1000000000
Output
11 3
0 1000000000
NoteExplanation for the sample input/output #1For 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).
5 3
ABAAA
2 1 5 1 1
1 3 5
2 2 5 0 1000000000

11 3 0 1000000000 
['data structures', 'math', 'matrices', '*2100']