Astonishing Numbers

In this challenge, you have to establish if a given integer is an Astonishing number. An Astonishing number is an integer that, when partitioned into two parts a (left) and b (right), is equal to the sum of the consecutive numbers from a up to b (if a is lower than b), or from b up to a (if a is greater than b).

Given a positive integer num, implement a function that returns:

• The string "AB-Astonishing" if num is an Astonishing number and the partition a is lower than b.
• The string "BA-Astonishing" if num is an Astonishing number and the partition a is greater than b.
• false if num is not an Astonishing number.

Examples

isAstonishing(15) ➞ "AB-Astonishing"
// There is only one possible partition: a = 1 and b = 5
// Sum from a up to b: 1 + 2 + 3 + 4 + 5 = 15
// It's Astonishing and partition a is lower than partition b

isAstonishing(4020) ➞ false
// There are three possible partitions
// Partition 1: a = 4 and b = 020 = 20 (leading zeros are not considered)
// Sum from a up to b: 4 + 5 + 6 + ... + 20 = 204
// Partition 2: a = 40 and b = 20
// Sum from b up to a: 20 + 21 + 22 + ... + 40 = 630
//Partition 3: a = 402 and b = 0
// Sum from b to a: 0 + 1 + 2 + ... + 402 = 81003
// It's not Astonishing

isAstonishing(2002077) ➞ "BA-Astonishing"
// There are six possible partitions
// Partition 1: a = 2 and b = 002077 = 2077 (leading zeros are not considered)
// Sum from a up to b: 2 + 3 + 4 + ... + 2077 = 2158002
// Partition 2: a = 20 and b = 02077 = 2077
// Sum from a up to b: 20 + 21 + 22 + ... + 2077 = 2157813
// Partition 3: a = 200 and b = 2077
// Sum from a up to b: 200 + 201 + 202 + ... + 2077 = 2138103
// Partition 4: a = 2002 and b = 077 = 77
// Sum from b up to a: 77 + 78 + 79 + ... + 2002 = 2002077
// It's Astonishing and partition a is greater than partition b

Notes

• Leading zeros in the b partition are not considered (see examples #2 and #3).
• A valid partition has at least a number into it, and this number can be also 0 (see example #2).
• You can expect positive integers greater than 9 as input (a single-digit number can't be partitioned).