#### Extended Euclidean GCD

```/**
* Problem statement and explanation: https://en.wikipedia.org/wiki/Extended_Euclidean_algorithm
*
* This algorithm plays an important role for modular arithmetic, and by extension for cyptography algorithms
*
* Basic explanation:
* The Extended Euclidean algorithm is a modification of the standard Euclidean GCD algorithm.
* It allows to calculate coefficients x and y for the equation:
*          ax + by = gcd(a,b)
*
* This is called Bézout's identity and the coefficients are called Bézout coefficients
*
* The algorithm uses the Euclidean method of getting remainder:
* r_i+1 = r_i-1 - qi*ri
* and applies it to series s and t (with same quotient q at each stage)
* When r_n reaches 0, the value r_n-1 gives the gcd, and s_n-1 and t_n-1 give the coefficients
*
* This implementation uses an iterative approach to calculate the values
*/

/**
*
* @param {Number} arg1 first argument
* @param {Number} arg2 second argument
* @returns Array with GCD and first and second Bézout coefficients
*/
const extendedEuclideanGCD = (arg1, arg2) => {
if (typeof arg1 !== 'number' || typeof arg2 !== 'number') throw new TypeError('Not a Number')
if (arg1 < 1 || arg2 < 1) throw new TypeError('Must be positive numbers')

// Make the order of coefficients correct, as the algorithm assumes r0 > r1
if (arg1 < arg2) {
const res = extendedEuclideanGCD(arg2, arg1)
const temp = res
res = res
res = temp
return res
}

// At this point arg1 > arg2

// Remainder values
let r0 = arg1
let r1 = arg2

// Coefficient1 values
let s0 = 1
let s1 = 0

// Coefficient 2 values
let t0 = 0
let t1 = 1

while (r1 !== 0) {
const q = Math.floor(r0 / r1)

const r2 = r0 - r1 * q
const s2 = s0 - s1 * q
const t2 = t0 - t1 * q

r0 = r1
r1 = r2
s0 = s1
s1 = s2
t0 = t1
t1 = t2
}
return [r0, s0, t0]
}

export { extendedEuclideanGCD }
```  