Check Digits

Books, groceries, bank accounts, and credit cards are all identified mainly by a number, and those numbers often run to many digits. Transcribing one is easy to get wrong, so most numbering schemes carry a mechanism that detects errors and sometimes corrects them.

The simplest scheme appends a single check digit. Multiply the rightmost digit by $2$, the digit to its left by $3$, and so on, raising the weight by $1$ at every step to the left, then add all the products. Divide that sum by $11$ and subtract the remainder from $11$. If the result lies between $1$ and $9$, append it to the right end of the number. If the result is $11$, append the digit $0$ as the check digit. If the result is $10$, reject the original number.

To test whether a complete number is correct, multiply successive digits from the right by $1$, $2$, $3$, ... and add the products. The number is good when that sum is divisible by $11$, and bad otherwise.

Take the number $2763$. Multiply $3$ by $2$ to get $6$; multiply $6$ by $3$ to get $18$ and add for $24$; multiply $7$ by $4$ to get $28$ and add for $52$; multiply $2$ by $5$ to get $10$ and add for $62$. Dividing $62$ by $11$ leaves a remainder of $7$, and $11$ minus $7$ gives the check digit $4$, so the full number is $27634$. Check for yourself that the test works in the other direction, and that changing any digit, or even swapping two digits, makes the number bad.

Write a program that reads a series of numbers, each at most $15$ digits long, and produces the check digit for each one.

The input is a series of numbers, one per line. Each number consists of decimal digits only with no embedded whitespace, and is at least $1$ and at most $15$ digits long. The input ends with a line containing a single #.

Print one line for every number in the input, excluding the terminating #. Each line holds the original number, then the four characters ->, then either the check digit or the word Rejected.