bool binSearch(double a[], double q, int l, int r){
//ARG: (1) Elements in a are increasingly sorted.
//     (2) 0 <= l <= r < length(a)
//DESC: return-value == true, if there is an index i, s <= i <= t
//      such that q == a[i]. Otherwise return-value == false.
  if (l == r)
    return (q == a[l]);

  int m = (l+r)/2;
  if (q == a[m])
    return true;

 if (q < a[m])
    return binSearch(a, q, l, m);
  else
    return binSearch(a, q, m+1, r);
}