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

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