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:
function f(L, R, A, B):
FOR i from L to R
if S[i] = 'A'
A = A + B
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.
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 $$$1\,000\,000\,007$$$.
5 3 ABAAA 2 1 5 1 1 1 3 5 2 2 5 0 1000000000
11 3 0 1000000000
Explanation for the sample input/output #1
For the first command, calling $$$f(L, R, A, B)$$$ causes the following:
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 $$$(0, 1\,000\,000\,000)$$$.