Some bugs that I cant discover

[dickmw]

I am new to programming (or perhaps computer)
And I just started learning C++ yesterday.
While I try to make up a program that generates fibonacci sequence, it gives negative value when the amount of terms generated is large.
The code is as follows:

1 #include <iostream>
2 using namespace std;
3 int x,y,z,a;
4 int main()
5 {
6 cout<<"This program is for generating fibonacci sequence;\nPlease initialize the conditions\n";
7 cin>>x>>y; // x is the 1st term while y is the 2nd term
8 cin.ignore();
9 cout<<"Please limit the amount of numbers generated\n";
10 cin>>z; //z refers to the number of terms calculated
11 cin.ignore();
12 a=1;
13 cout<<"T("<<a<<")="<<x<<"\n";
14 cout<<"T("<<(a+1)<<")="<<y<<"\n";
15 while (a<z)
16 {
17 a++;
18 x+=y;
19 cout<<"T("<<a<<")="<<x<<"\n";
20 a++;
21 if (a<=z){
22 y+=x;
23 cout<<"T("<<(a)<<")="<<y<<"\n";}
24
25 }
26 cout<<"Sequence terminates";
27 cin.get();
28
29 }

The numbers refer to the number of lines
I input 1 1 for the first input (for x and y)and then 100 for the second input (for z)
Hope that anyone can save me

[firedraco]

That's because an int can only hold so much data. You'd need to use a large type like a long int. Eventually you will run out of space though. In that case you would need to use a bignum library.