To store the number of variables with ith bit set
int p ; if ( x1 == 0 and y1 == 0 ) p = prefix_count [ i ] [ x2 ] [ y2 ] ; else if ( x1 == 0 ) p = prefix_count [ i ] [ x2 ] [ y2 ] - prefix_count [ i ] [ x2 ] [ y1 - 1 ] ; else if ( y1 == 0 ) p = prefix_count [ i ] [ x2 ] [ y2 ] - prefix_count [ i ] [ x1 - 1 ] [ y2 ] ; else p = prefix_count [ i ] [ x2 ] [ y2 ] - prefix_count [ i ] [ x1 - 1 ] [ y2 ] - prefix_count [ i ] [ x2 ] [ y1 - 1 ] + prefix_count [ i ] [ x1 - 1 ] [ y1 - 1 ] ;