You are given a very large integer n, represented as a string,​​​​​​ and an integer digit x. The digits in n and the digit x are in the inclusive range [1, 9], and n may represent a negative number.

AddDigitGetMaxValue.kt

package org.kotlinlang.play

import java.math.BigInteger

fun main() {
    val input = mapOf(
        -999 to -5999,
        999 to 9995,
        9643 to 96543
    )
    val added = 5
    
    input.keys.forEach {
        val result = maxValue(it, added)
        println(result)
    }
}

fun maxValue(N: Int, K: Int): String {
    val digits = N.toString().toCharArray()
    val probability = mutableListOf<BigInteger>()

    val hasSign = digits.first() == '-'
    val startFrom = if (hasSign) 1 else 0

    for (index in startFrom until digits.size) {
        val startNumber = digits.copyOfRange(0, index)
        val endNumber = digits.copyOfRange(index, digits.size)
        val newNumber = mutableListOf<Char>()

        newNumber.addAll(startNumber.toList())
        newNumber.add(index, ('0' + K))
        newNumber.addAll(endNumber.toList())
        probability.add(newNumber.toCharArray().joinToString("").toBigInteger())
    }
    probability.add("$N$K".toBigInteger())

    return probability.max().toString()
}

Playground:
https://pl.kotl.in/x4HUYVIrD

Leetcode:
https://leetcode.com/problems/maximum-value-after-insertion/submissions/

Note: It's not optimise for big numbers