【NOIP2016练习】T2 跑跑步 （数论）

：

这场的难度是从高到低的

 var a:array[..]of longint;
     n,m,i,ans:longint;

 function gcd(x,y:longint):longint;
 var r:longint;
 begin
  repeat
   r:=x mod y;
   x:=y;
   y:=r;
  until r=;
  exit(x);
 end;

 function fi(x:longint):longint;
 var i:longint;
 begin
  fi:=x;
  for i:= to trunc(sqrt(x)) do
   if x mod i= then
   begin
    fi:=fi div i*(i-);
    while x mod i= do x:=x div i;
   end;
  if x> then fi:=fi div x*(x-);
 end;

 function clac(x:longint):longint;
 var i:longint;
 begin
  for i:= to m do
   if x mod gcd(n,a[i])= then exit(fi(n div x));
  exit();
 end;

 begin
  assign(input,'1.in'); reset(input);
  assign(output,'1.out'); rewrite(output);
  readln(n,m);
  for i:= to m do read(a[i]);
  for i:= to trunc(sqrt(n)) do
   if n mod i= then
   begin
    ans:=ans+clac(i);
    if i*i<>n then ans:=ans+clac(n div i);
   end;
  writeln(n-ans);

  close(input);
  close(output);
 end.