Here's something that has caught my attention when hovering over their profiles – their user IDs are \$31716\$ and \$45941\$. If you perform digit-wise subtraction, you'll notice something pretty exciting (of course, taking the absolute differences):
3|1|7|1|6 4|5|9|4|1 -+-+-+-+- (-) 1|4|2|3|5
The number generated by the above algorithm is \$14235\$. There is something special about this integer: It consists of consecutive digits only, sorted in ascending order, but exactly one of the digits is not placed correctly — \$4\$.
We will call a pair of positive integers \$(a, b)\$ a DJMcMego pair if the digit-wise absolute differences are consecutive integers, sorted in ascending order, but exactly one of them is not where it belongs. That is, it is possible to move exactly one digit of the result of digit-wise subtraction to another position, such that the integer obtained only has consecutive digits, sorted in ascending order.
In our example above, the pair \$(31716, 45941)\$ is a DJMcMego pair, because if \$4\$ is moved between \$3\$ and \$5\$, the result is \$12345\$, which fulfils the criteria. Note that the digits of the resulting number do not need to start at \$1\$, they just ought to be consecutive. When one is unsure about what decision they should make, they can always rely on the other's help to sort things out.
Your task is to output a truthy/falsy value depending on whether a pair of positive integers given as input is a DJMcMego pair.
You are guaranteed that \$a\$ and \$b\$ will have the same number of digits, always at least 4.
You can take the integers in any reasonable format (i.e. native integers, strings, lists of digits, etc.)
You can compete in any programming language and can take input and provide output through any standard method, while taking note that these loopholes are forbidden by default. This is code-golf, so the shortest submission (in bytes) for every language wins.
a, b -> Output 31716, 45941 -> Truthy 12354, 11111 -> Truthy 56798, 22222 -> Truthy 23564, 11111 -> Truthy 1759, 2435 -> Truthy 12345, 11111 -> Falsy 3333, 2101 -> Falsy 22354, 22222 -> Falsy 31717, 45941 -> Falsy 14325, 11111 -> Falsy 89789, 78865 -> Falsy 14954, 61713 -> Falsy 25631, 11114 -> Falsy
Or, in another format.