poj2115 C Looooops 空间 2012-01-14

http://poj.org/problem?id=2115

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求 a+cx=b (mod 2^k)

用exgcd求线性模方程！

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Program Stone;
var i:longint;
    a,b,c,k,x,y,g,ans:int64;
    sh:array[0..50]of int64;

 Function exgcd(a,b:int64;var x,y:int64):int64;
 var i:int64;
  begin
     if b=0 then begin x:=1;y:=0;exit(a);end;
     exgcd:=exgcd(b,a mod b,x,y);
     i:=x;
     x:=y;
     y:=i-(a div b)*y;
  end;
begin
  assign(input,'input.in');reset(input);
  sh[0]:=1;
  for i:=1 to 32 do sh[i]:=sh[i-1]*2;
  readln(a,b,c,k);
  while (a<>0)or(b<>0)or(c<>0)or(k<>0) do
   begin
     g:=exgcd(c,sh[k],x,y);
     if (b-a) mod g<>0 then writeln('FOREVER')
                       else begin
                              ans:=x*(b-a) div g mod sh[k]+sh[k];
                              writeln(ans mod (sh[k] div g));
                            end;
     readln(a,b,c,k);
   end;
end.