I've passed this problem with time 0.125 ! And the only mathematical conclusion I used is that when x is a square root then (n-x) is also.

I am sure that the mathematical approach to this problem is also interesting (and probably harder than mine) but it was still very interesting for me to find the way to solve this problem without using of deep math knowledge.
It is also interesting that my solution runs faster then some implementing the math approach :-) but still I use much  more memory...

http://acm.timus.ru/status.aspx?space=1&num=1132&author=30467

Thanks to mr. Medvedev for this problem.

program Ural_1132;
var
  i,j,x,p,q,n:longint;

function power(a,b,c:longint):longint;
var
  d,s:longint;
begin
  d:=a;s:=1;
  while b>0 do
  begin
    if odd(b) then s:=(s*d) mod c;
    b:=b div 2;d:=(d*d) mod c;
  end;
  exit(s);
end;

begin
  read(n);
  for i:=1 to n do
  begin
    read(q,p);q:=q mod p;
    if (p=2) and (q=1) or (p<>2) and (power(q,(p-1) div 2,p)=p-1) then
    begin
      writeln('No root');
      continue;
    end;
    if trunc(sqrt(q))=0 then
    begin
      x:=trunc(sqrt(q));
      write(x);
      if p-x<>x then write(' ',p-x);
      writeln;
      continue;
    end;
    for j:=1 to (p-1) div 2 do
    begin
      x:=(j*j) mod p;
      if x=q then
      begin
        write(j);
        if p-j<>j then write(' ',p-j);
        writeln;
        break;
      end;
    end;
  end;
end.

Edited by author 07.03.2007 18:27