problem in understanding limit for value of "a" in NUKES problem?

The problem NUKES, in this problem the value of “a” can range up to 1000000000 but some programmers have used integer array to store the values of a,n and k and still got accepted.
you can see it in this problem. How is this possible.

You can store up to approximately 10^9 in integers.

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not possible in c language, integer ranges upto 32767

Nop dude. In gcc int is 4 bytes. Google it.

Size of int is not strictly specified in the C standards. The standards guarantees only that char is at least 8 bits, int at least 16-bit, long at least 32-bit and long long at least 64-bit (or something equivalent to those capacities). The typical distribution is {8,32,64,64}, but I’ve run into issues before with an old judging system running 32-bit SPARC where it is {8,32,32,64}. I would be surprised though is you found any judge system where int is 16-bit.