【NOIP2016练习】T2 跑跑步 （数论）

：

这场的难度是从高到低的

var a:array[1..100]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=0;
 exit(x);
end;

function fi(x:longint):longint;
var i:longint;
begin
 fi:=x;
 for i:=2 to trunc(sqrt(x)) do
  if x mod i=0 then
  begin
   fi:=fi div i*(i-1);
   while x mod i=0 do x:=x div i;
  end;
 if x>1 then fi:=fi div x*(x-1);
end;

function clac(x:longint):longint;
var i:longint;
begin
 for i:=1 to m do
  if x mod gcd(n,a[i])=0 then exit(fi(n div x));
 exit(0);
end;

begin
 assign(input,'1.in'); reset(input);
 assign(output,'1.out'); rewrite(output);
 readln(n,m);
 for i:=1 to m do read(a[i]);
 for i:=1 to trunc(sqrt(n)) do
  if n mod i=0 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.