Odious Numbers


An odious number is a nonnegative number that has an odd number of 1s in its binary representation. The first few odious numbers are therefore 1, 2, 4, 7, 8, 11, 13, 14, 16, 19… Numbers that are not odious are said to be evil numbers.

Problem

Decide which numbers, in a given closed interval, are odious numbers, and find all pairs of consecutive numbers (n,n+1), where n is both an odious and an odd number and n+1 is both an evil and an even number: (odious_odd,evil_even).

Input

The input has one line containing two positive integers between 1 and 10000 each, separated by a space; the first integer – L – is the low limit of the closed interval; the second one – H – is the high limit.

Output

The output is composed of the pairs of consecutive numbers oe(odious_odd,evil_even) and the set of odious numbers in the form o{o1,o2,o3…} that lie in the interval [L,H].

There must be a line for each pair oe(odious_odd,evil_even) and a final line with the set of odious numbers. In the absence of resulting pairs, no line is written for the pairs. In the absence of resulting odious numbers, the last line contains the empty set o{}.

Sample Input 1

1 20

Sample Output 1

oe(11,12)
oe(19,20)
o{1,2,4,7,8,11,13,14,16,19}

Sample Input 2

3 3

Sample Output 2

o{}