const eps=0.000001;
var i,n:word; a,b:real;
begin
readln(n);
for i:=1 to n do begin
readln(b);
a:=(sqrt(8*b-7)-1)/2;
if (frac(a)<eps) or (frac(a)>1-eps) then write('1 ')
else write('0 ');
end;
end.

Thank you very much!

Can anyone explain how does it give the right answers?

can you please explain the logic of the problem?