Reduce a Power Given Decimal Exponent Digits
Company: Google
Role: Software Engineer
Category: Coding & Algorithms
Difficulty: medium
Interview Round: Other
# Reduce a Power Given Decimal Exponent Digits
Given a positive integer `a` and a list `b` containing the decimal digits of a positive exponent, return `a` raised to that exponent, modulo `1337`.
The exponent may contain up to `2000` digits.
### Function
`int superPow(int a, vector<int>& b)`
### Example 1
```text
Input: a = 3, b = [4]
Output: 81
```
### Example 2
```text
Input: a = 2, b = [1,1]
Output: 711
```
The exponent is `11`. The remainder of `2048` divided by `1337` is `711`.
### Example 3
```text
Input: a = 1337, b = [2]
Output: 0
```
### Constraints
- `1 <= a <= 2147483647`.
- `1 <= b.length <= 2000`.
- `0 <= b[i] <= 9`.
- `b` has no leading zero and represents a positive integer.
### Clarifications
The digits are supplied most significant first. Return a remainder in the range `0` through `1336`; do not return the full power. No assumption that `a` is relatively prime to `1337` is given.
### What a Strong Answer Covers
- Correct interpretation of the exponent digits.
- Handling an exponent too large for ordinary integer types.
- Correct remainders for all allowed bases.
- A correctness argument and numeric/time/storage bounds.
Overview: Practice evaluating a modular power whose positive exponent is supplied as decimal digits. Handle long exponents, place value, and all permitted bases safely.