Fibonacci and the C++ conundrum

DISCLAIMER: the following Blog post involves computer programming. If this sort of thing bores you or confuses you, you might as well not read any further and instead I advise you to check out something nonsensical like LOLCATS. I wouldn't want to ruin your interweb experience.
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I was wondering how difficult it would be to write a program that would calculate the fibonacci sequence. After giving it a bit of thought, I decided that it didn't seem too hard, so I wrote the program using C++ and compiled the code using Dev C++.




The code seems simple enough. It looks like this:

#include iostream
#include stdlib.h
using namespace std;

int main(){

int first, second, num1,num2,num3;
int index=1;

first=1;
second=1;

do{
num1=first;
num2=second;

num3=num1+num2;

cout<< num1 <<" ";
index++;

first=num2;
second=num3;

}while(index<=45);

cin.get();
return 0;
}

Unfortunately.... things didn't go EXACTLY as planned....



If the 'do loop' is executed 'while(index<=45);' , everything goes according to plan:



But if I start putting in larger numbers, like 'while(index<=65);' BAD things start to happen:



This is quite unfortunate, because I was really hoping to see the hundredth fibonacci number. I can't explain why, I just really had my heart set on it.

Low numbers of iterations work PERFECTLY fine, but larger numbers (anything after 46 iterations) will start giving me negative numbers.

If anyone reading this is a programmer, and sees a problem with the logic, please let me know what I did wrong.

oh.... I know it might be the compilers fault, but I'm too lazy to search the web for another free compiler. K THNX BI !11!