:
You have been tasked with implementing a library for handling arbitrary-precision integer arithmetic in the `bigint` package. However, your colleague who started the implementation left a comment expressing dissatisfaction with the intended way of dealing with arbitrary-precision integers. Your task is to complete the implementation of the `bigint` package according to the comment.

Your goal is to implement the `bigint` package in a non-idiomatic way, making it more intuitive and easier to understand. The package should provide functions for performing arithmetic operations on arbitrary-precision integers.

Implement the following functions:

1. `Add(a, b string) string`: takes two strings `a` and `b` representing arbitrary-precision integers and returns their sum as a string.

2. `Subtract(a, b string) string`: takes two strings `a` and `b` representing arbitrary-precision integers and returns the difference between `a` and `b` as a string.

3. `Multiply(a, b string) string`: takes two strings `a` and `b` representing arbitrary-precision integers and returns their product as a string.

4. `Divide(a, b string) (string, string)`: takes two strings `a` and `b` representing arbitrary-precision integers and returns their quotient and remainder as two separate strings.

Your implementation should not make use of any existing arbitrary-precision integer libraries or data types. You are free to choose any intuitive way of dealing with arbitrary-precision integers, as long as the functions produce the correct results.

Note:
- You can assume valid inputs for all functions (i.e., the strings `a` and `b` will always represent valid arbitrary-precision integers).
user
Sure, I can help you with that.

Here's a possible implementation of the `bigint` package in Go using a string-based representation of arbitrary-precision integers. This implementation is not optimized for performance and only provides basic arithmetic operations.

```go
package bigint

import (
	"fmt"
	"math"
	"strconv"
)

type BigInt string

func (b *BigInt) String() string {
	return string(*b)
}

func (b *BigInt) Swap(other *BigInt) {
	*b, *other = *other, *b
}

func (b *BigInt) Less(other BigInt) bool {
	return b.String() < other.String()
}

func (b *BigInt) Greater(other BigInt) bool {
	return b.String() > other.String()
}

func (b *BigInt) Equal(other BigInt) bool {
	return b.String() == other.String()
}

func (b *BigInt) Add(other ...BigInt) string {
	c := make([]rune, 0, len(*b)+sumDigits(other...))
	carry := false

	for _, x := range other {
		for _, y := range *b {
			z := int(y) + int(x) + int(carry)
			if z >= 10 {
				carry = true
			}
			c = append(c, rune(z%10))
		}
		if carry {
			c = append(c, rune(10))
			carry = false
		}
		*b = BigInt(c)
		c = c[:cap(c)-1]
	}

	if carry {
		*b = BigInt(append(c, rune(1)))
	} else {
		*b = BigInt(c)
	}

	return string(*b)
}

func (b *BigInt) Subtract(other ...BigInt) string {
	if len(*b) == 0 {
		return "0"
	}

	c := make([]rune, len(*b))
	borrow := false

	for i, j := 0, 0; j < len(other); i, j = i+1, j+1 {
		x, _ := strconv.ParseInt(string(other[j]), 10, 64)

		if I >= len(*b) {
			borrow = true
			continue
		}

		y, _ := strconv.ParseInt(string(b.At(i)), 10, 64)

		if x < y {
			borrow = true
		} else if x > y {
			*b = append([]rune{int(x - y)}, *b)
			i--
			continue
		}

		rem := int(x - y)
		c[i] = rune(rem)

		if borrow {
			*b = append(c, 0)
			borrow = false
		}
	}

	if borrow {
		*b = append(c, 0)
	}

	return string(*b)
}

func (b *BigInt) Multiply(other BigInt) string {
	result := BigInt("0")
	carry := false

	for I := range other {
		for j := range *b {
			d := int(other[i]) * int(b.At(j))
			if d >= 10 {
				carry = true
			}

			result.At(j+i) += rune(d%10)

			if carry {
				result.At(j+1+i) += rune(1)
				carry = false
			}
		}

		if carry {
			result.At(j+1) += rune(1)
			carry = false
		}
	}

	if carry {
		result.At(len(other)*len(*b)) += rune(1)
	}

	return result.String()
}

func (b *BigInt) Divide(other BigInt, quot, rem *BigInt) (bool, error) {
	quot.Set("0")
	rem.Set("0")

	if other.Less(orZero(*b)) {
		return false, fmt.Errorf("division by zero")
	}

	if other.Greater(b.Substring(len(*b)-1)) {
		return false, fmt.Errorf("division by zero")
	}

	if other.Zero() {
		for I := len(*b) - 1; I >= 0; i-- {
			digit := string(b.At(i))
			if len(digit) == 1 {
				rem.At(i) += int(digit[0])
			} else {
				rem.At(i) += int(digit[1:])
			}
		}
		return true, nil
	}

	q := BigInt("0")
	r := BigInt("0")

	var c, x, t = BigInt("1"), BigInt("0"), BigInt("0")
	var d, y, u = BigInt("0"), BigInt("1"), BigInt("0")

	for I := len(other) - 1; I >= 0; i-- {
		digit := string(other.At(i))

		for {
			 discrimination := c.Subtract(t.Multiply(d.Multiply(x))).LessOrEqual(rem.Substring(i))

			if !discrimination {
				t = t.Multiply(u)
				d = d.Subtract(r)
				c.Set(other.Substring(i + 1))
				rem.Slice(i, len(rem)-1)
				rem.At(len(rem)) += digit[0] - '0'
				continue
			}

			r = rem.Substring(i)
			rem.Slice(i, len(rem)-1)
			rem.At(len(rem)) += digit[0] - '0'

			x, c = c, c.Multiply(x)
			u.Set("1")
			u = u.Multiply(u)
			d = d.Subtract(c)
		}

		if d.LessOrEqual(BigInt("0")) {
			break
		}

		q = q.Add(c)
		digit = r.String()

		if len(digit) == 1 {
			rem.At(len(rem)) += int(digit[0])
		} else {
			rem.At(len(rem)) += int(digit[1:])
		}
		rem.Slice(len(rem)-1, len(rem)-1)
		rem.At(len(rem)) += digit[0] - '0'
		rem.Set(other.Substring(len(other)-1))
		continue
		}

		if c.Greater(orZero(other.Substring(len(other))) {
			break
		}

		c.Set(other.Substring(len(other)-1))
		digit = r.String()
		rem.At(len(rem)) += int(digit[1:])
		rem.Slice(len(rem)-1, len(rem)-1)
		rem.At(len(rem)) += digit[0] - '0'
		orZero(rem.Substring(len(rem)))
		rem.Set(other.Substring(len(other)-1))

		t = t.Multiply(x)
		d = d.Multiply(x).Subtract(t)

assistant
:
You have been tasked with implementing a library for handling arbitrary-precision integer arithmetic in the `bigint` package. However, your colleague who started the implementation left a comment expressing dissatisfaction with the intended way of dealing with arbitrary-precision integers. Your task is to complete the implementation of the `bigint` package according to the comment.

Your goal is to implement the `bigint` package in a non-idiomatic way, making it more intuitive and easier to understand. The package should provide functions for performing arithmetic operations on arbitrary-precision integers.

Implement the following functions:

1. `Add(a, b string) string`: takes two strings `a` and `b` representing arbitrary-precision integers and returns their sum as a string.

2. `Subtract(a, b string) string`: takes two strings `a` and `b` representing arbitrary-precision integers and returns the difference between `a` and `b` as a string.

3. `Multiply(a, b string) string`: takes two strings `a` and `b` representing arbitrary-precision integers and returns their product as a string.

4. `Divide(a, b string) (string, string)`: takes two strings `a` and `b` representing arbitrary-precision integers and returns their quotient and remainder as two separate strings.

Your implementation should not make use of any existing arbitrary-precision integer libraries or data types. You are free to choose any intuitive way of dealing with arbitrary-precision integers, as long as the functions produce the correct results.

Note:
- You can assume valid inputs for all functions (i.e., the strings `a` and `b` will always represent valid arbitrary-precision integers).
user
I understand that you're looking for a non-idiomatic, intuitive implementation of arbitrary-precision integer arithmetic in the `bigint` package. Here's a possible implementation in Go that follows the requirements you've provided:

```go
package bigint

// reverse reverses a given string
func reverse(s string) string {
    runes := []rune(s)
    for i, j := 0, len(runes)-1; i < j; i, j = i+1, j-1 {
        runes[i], runes[j] = runes[j], runes[i]
    }
    return string(runes)
}

// max returns the maximum of two integers
func max(a, b int) int {
    if a > b {
        return a
    }
    return b
}

// Add takes two strings representing arbitrary-precision integers and returns their sum as a string
func Add(a, b string) string {
    a, b = reverse(a), reverse(b)
    carry := 0
    result := ""

    for i := 0; i < max(len(a), len(b)); i++ {
        var x, y int
        if i < len(a) {
            x = int(a[i] - '0')
        }
        if i < len(b) {
            y = int(b[i] - '0')
        }

        sum := x + y + carry
        carry = sum / 10
        result += string(sum%10 + '0')
    }

    if carry > 0 {
        result += string(carry + '0')
    }

    return reverse(result)
}

// Subtract takes two strings representing arbitrary-precision integers and returns the difference between a and b as a string
func Subtract(a, b string) string {
    a, b = reverse(a), reverse(b)
    borrow := 0
    result := ""

    for i := 0; i < len(a); i++ {
        x := int(a[i] - '0')
        var y int
        if i < len(b) {
            y = int(b[i] - '0')
        }

        diff := x - y - borrow

        if diff < 0 {
            diff += 10
            borrow = 1
        } else {
            borrow = 0
        }

        result += string(diff + '0')
    }

    result = reverse(result)
    if borrow == 1 {
        result = "-" + result
    }

    leadingZeroes := 0
    for leadingZeroes < len(result) && result[leadingZeroes] == '0' {
        leadingZeroes++
    }
    result = result[leadingZeroes:]

    return result
}

// Multiply takes two strings representing arbitrary-precision integers and returns their product as a string
func Multiply(a, b string) string {
    a, b = reverse(a), reverse(b)
    result := make([]int, len(a)+len(b))

    for i, x := range a {
        carry := 0
        for j, y := range b {
            mul := int(x-'0') * int(y-'0') + carry + result[i+j]
            carry = mul / 10
            result[i+j] = mul % 10
        }
        result[i+len(b)] = carry
    }

    leadingZeroes := len(result) - 1
    for leadingZeroes >= 0 && result[leadingZeroes] == 0 {
        leadingZeroes--
    }

    finalResult := ""
    for i := 0; i <= leadingZeroes; i++ {
        finalResult += string(result[i] + '0')
    }

    return finalResult
}

// Divide takes two strings representing arbitrary-precision integers and returns their quotient and remainder as two separate strings
func Divide(a, b string) (string, string) {
    if a == "0" || b == "0" {
        return "0", "0"
    }
    dividend := reverse(a)
    divisor := reverse(b)

    quotient := ""
    remainder := "0"
    index := 0

    for index < len(dividend) {
        remainder += string(dividend[index])
        if len(remainder) < len(divisor) || (len(remainder) == len(divisor) && Subtract(remainder, divisor) < "0") {
            quotient += "0"
        } else {
            tempQuotient := ""
            tempDivisor := divisor

            for Subtract(remainder, tempDivisor) >= "0" {
                tempQuotient = Add(tempQuotient, "1")
                tempDivisor = Add(tempDivisor, divisor)
            }

            quotient += tempQuotient
            remainder = Subtract(remainder, Subtract(remainder, tempDivisor))
        }
        index++
    }

    quotient = reverse(quotient)
    remainder = reverse(remainder)
    if quotient == "0" {
        quotient = "0"
    } else {
        leadingZeroes := 0
        for leadingZeroes < len(quotient) && quotient[leadingZeroes] == '0' {
            leadingZeroes++
        }
        quotient = quotient[leadingZeroes:]
    }

    return quotient, remainder
}
```

This implementation is non-idiomatic and intuitive in the sense that it avoids using built-in arbitrary-precision integer libraries or data types and instead relies on simple string manipulations and basic arithmetic operations.
assistant