【问题描述】
A number sequence is defined as follows:

f(1) = 1, f(2) = 1, f(n) = (A * f(n - 1) + B * f(n - 2)) mod 7.

Given A, B, and n, you are to calculate the value of f(n).

【解题报告】
因为是mod 7，所以说最多有49种可能。数据范围太大，不能用裸搜，于是找循环点。
 1 program number;
 2 
 3 var
 4   h:array[0..50]of longint;
 5   t:array[0..7,0..7]of longint;
 6   a,b,n,i,j,w,s:longint;
 7   can:boolean;
 8 
 9 procedure init;
10 begin
11   assign(input,'number.in');
12   reset(input);
13   assign(output,'number.out');
14   rewrite(output);
15 end;
16 
17 procedure outit;
18 begin
19   close(input);
20   close(output);
21   halt;
22 end;
23 
24 procedure main;
25 begin
26   repeat
27     fillchar(t,sizeof(t),0);
28     can:=false;
29     readln(a,b,n);
30     if (a+b+n=0) then outit;
31     h[1]:=1;
32     h[2]:=1;
33     for i:=3 to n do
34     begin
35       if t[h[i-1],h[i-2]]<=0 then
36       begin
37         h[i]:=(h[i-1]*a+h[i-2]*b)mod 7;
38         t[h[i-1],h[i-2]]:=i;
39       end
40       else
41       begin
42         s:=t[h[i-1],h[i-2]]-2;
43         can:=true;
44         w:=i-s-2;
45         for j:=1 to w-1 do h[j]:=h[j+s-1];
46         h[0]:=h[w+s-1];
47         break;
48       end;
49     end;
50     if not can then writeln(h[n]) else writeln(h[(n-s+1)mod w]);
51   until seekeof;
52 end;
53 
54 begin
55   init;
56   main;
57   outit;
58 end.
59