For loop get iteration number using only i and j

Question

I ran through questions with similar titles but could not find them anywhere. Suppose I have a for loop (regardless of the programming language)

for (i=0; i < n; i++)
    for (j=0; j < m; j++)
        k = ...
        print("k is: " + k)

I now want to calculate k based ONLY on i and j where k is the iteration count. So for example when n=2 and m=2 than we should get

k is 0
k is 1
k is 2
k is 3

Is this possible only using i and j or do I need to introduce another variable which gets incremented each time? This question is more theoretical as one can always simply solve an actual problem by using a counter. Note: starting at one in the print is also good.

Answer 1

You cannot do it without knowing either m or n

k = i * m + j

Or

k = i + j * n

And to start by 1:

k = i * m + j + 1

or

k = i + j * n + 1