Full Stack Engineer

Alex is having a problem with his keyboard. If he presses any key, he may get extra occurrences of that character. Example: If he wants to write "hey", he may end up typing: hhey, hheey, heey, hhheyyy, etc.

You are given a string 'S' typed by Alex. Your task is to find out the number of possible strings Alex was trying to type and return the same.

Output can be very large. Return (number of ways % 1e9 + 7). Where % is the modular operator.

For Example :

Let 'S' = "adddef".
Alex could have been trying to type:
- "adef" (second and third 'd' are extra)
- "addef" (second 'd' is extra)
- "addef" (third 'd' is extra)
- "adddef" (no extra characters) 
So we have 3 distinct possibilities: "adef", "addef", and "adddef".
Therefore, the answer is 3.

Aahad and Harshit always have fun by solving problems. Harshit took a sorted array consisting of distinct integers and rotated it clockwise by an unknown amount. For example, he took a sorted array = [1, 2, 3, 4, 5] and if he rotates it by 2, then the array becomes: [4, 5, 1, 2, 3].

After rotating a sorted array, Aahad needs to answer Q queries asked by Harshit, each of them is described by one integer Q[i]. which Harshit wanted him to search in the array. For each query, if he found it, he had to shout the index of the number, otherwise, he had to shout -1.

For each query, you have to complete the given method where 'key' denotes Q[i]. If the key exists in the array, return the index of the 'key', otherwise, return -1.

Note:

Can you solve each query in O(logN) ?

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