Construct smallest number from I/D pattern

## Problem You are given a string `pattern` consisting only of the characters: - `'I'` meaning the next digit is **increasing** - `'D'` meaning the next digit is **decreasing** Construct the **numerically smallest** positive integer (as a string) that satisfies the pattern using **distinct digits** from `1` to `9`. Formally, if `pattern` has length `n`, you must output a string `ans` of length `n + 1` such that for every `i`: - if `pattern[i] == 'I'`, then `ans[i] < ans[i+1]` - if `pattern[i] == 'D'`, then `ans[i] > ans[i+1]` Digits cannot repeat, and you may only use digits `'1'` through `'9'`. ## Input - `pattern`: string of length `n` where `1 <= n <= 8` ## Output - The lexicographically/numerically smallest valid number as a string. ## Example - `pattern = "IID"` → output could be `"1243"` (since `1<2<4>3`).