{ Keszitette: Erdei Szabolcs 1997. erdeisz@dragon.klte.hu      }
program newton;
{A lagrange fele interpolacios alappolinom kiszamitasa Newton
    I. fromulajaval}
uses crt;
type valos = extended;
const maxy = 50;
var n: word;
    i: word;
    dy : array [1..maxy,1..maxy] of valos;
    fil : text;
    xo,vx,h,t : valos;
    l : valos;

procedure buildy;
var q,w : word;
  begin
    for w:=2 to n do
     for q:=1 to (n-w+1) do dy[q,w]:=dy[q+1,w-1]-dy[q,w-1];
  end;

procedure inputdata;
var e : word;
   begin
     assign(fil,'newton.inp');
     reset(fil);
     read(fil,n);
     for e:=1 to n do read(fil,dy[e,1]);
       readln(fil,xo);
     readln(fil,vx);
     read(fil,h);
     close(fil);
   end;

function fakt( alap : word) : valos;
var kuty : valos;
var r : word;
   begin
     kuty:=1;
     for r:=1 to alap do kuty:=kuty*r;
        fakt:=kuty;
   end;

procedure sett;
   begin
     t:=((vx-xo)/h);
   end;

function egyutth(tv: valos;kv : word) : valos;
var tmp : valos;
    y : word;
   begin
     tmp:=tv;
     if kv>=2 then for y:=2 to kv do tmp:=tmp*(tv-y+1);
       tmp:=tmp/fakt(kv);
     egyutth:=tmp;
   end;

procedure calculate;
var u : word;
   begin
     buildy;
     l:=0;
     for u:= 0 to n-1 do if u=0 then
       begin l:=l+dy[1,1]; writeln(u,': ',l); end
       else begin l:=l+egyutth(t,u)*dy[1,u+1]; writeln(u,': ',l); end;
   end;

begin
   clrscr;
   inputdata;
   sett;
   writeln;
   writeln('N erteke: ',n);
   for i:=1 to n do writeln('Y',i,' erteke: ',dy[i,1]:5:3);
     writeln('X0 erteke: ',xo:5:3);writeln('X erteke: ',vx:5:3);writeln('h erteke: ',h:5:3);
   writeln;
   buildy;
   calculate;
   writeln;
   writeln('L(',vx:5:2,')=',l:7:5);
   writeln;
end.