Can you explain how this C function works? It adds 2 numbers in BASE number system.
long int add(long int a, long int b) {
    long int sum=0;
    long int k=1;
    int c=0;
    while(a || b || c) {
        sum+=k*(c-c%BASE)/BASE;
        c=a%10+b%10;
        sum+=c%BASE*k;
        if(sum>=BASE*k)
        {
            c=5;
            sum-=BASE*k;
        }
        k*=10;
        a/=10;
        b/=10;
    }
    return sum;
}
This C function, add, takes two long integers a and b and returns their sum in a custom base number system. The base is not provided in the code you shared, so I will assume it is a constant named BASE. Here's a step-by-step explanation of the function:

1. Initialize the variables:
        * `sum`: The result of the addition, initialized to 0.
        * `k`: A multiplier used to keep track of the current digit position, initialized to 1.
        * `c`: A carry variable, initialized to 0.

2. The `while` loop continues as long as `a`, `b`, or `c` are non-zero:

    a. Add to `sum` the carry value c times the current digit position k, divided by `BASE`. This effectively adds the carry from the previous digit operation.

    b. Update the carry c with the sum of the least significant digits of a and b.

    c. Add to sum the least significant digit of the new carry c times the current digit position k.

    d. Check if the current partial sum in `sum` exceeds or equals `BASE * k`. If so, set the carry c to 5 and subtract `BASE * k` from sum. Note that this is an error in the function, as the carry should be set to 1, not 5. This could cause incorrect results in certain cases.

    e. Update the digit position k by multiplying it by 10.

    f. Divide a and b by 10 to remove their least significant digits.

3. Return the result of the addition, `sum`.

Please note that the code you provided contains an error in the carry handling logic. Instead of c = 5;, it should be c = 1; to correctly handle carry values in a base number system.
Could you correct the code and format it as a code block?
Here's the corrected and formatted code for the add function:

```c
long int add(long int a, long int b) {
    long int sum = 0;
    long int k = 1;
    int c = 0;

    while (a || b || c) {
        sum += k * (c - c % BASE) / BASE;
        c = a % 10 + b % 10;
        sum += c % BASE * k;

        if (sum >= BASE * k) {
            c = 1;
            sum -= BASE * k;
        }

        k *= 10;
        a /= 10;
        b /= 10;
    }

    return sum;
}
```
This version of the function sets the carry variable `c` to 1 instead of 5, which should correctly handle carry values in a base number system.