Problem: Little Victor adores the sets theory. Let us remind you that a set is a group of numbers where all numbers are pairwise distinct. Today Victor wants to find a set of integers S that has the following properties:

  * for all x <image> the following inequality holds l ≤ x ≤ r; 
  * 1 ≤ |S| ≤ k; 
  * lets denote the i-th element of the set S as si; value <image> must be as small as possible. 



Help Victor find the described set.

Input

The first line contains three space-separated integers l, r, k (1 ≤ l ≤ r ≤ 1012; 1 ≤ k ≤ min(106, r - l + 1)).

Output

Print the minimum possible value of f(S). Then print the cardinality of set |S|. Then print the elements of the set in any order.

If there are multiple optimal sets, you can print any of them.

Examples

Input

8 15 3


Output

1
2
10 11


Input

8 30 7


Output

0
5
14 9 28 11 16

Note

Operation <image> represents the operation of bitwise exclusive OR. In other words, it is the XOR operation.

Solution (in PYTHON):

Solution:
l,r,k=map(int,raw_input().split())
rs=[]
if k>=1: rs=[l]
if k>=2:
	if l+1==r:
		if l^(l+1)<l:rs=[l,r]
	else: rs=[l+(l&1),l+(l&1)+1]
if k>=3:
	cr=3*2**min(i-1 for i in xrange(70)if 2**i>l)
	if r>=cr: rs=[l,l^cr,cr]
if k>=4:
	if l+(l&1)+3<=r:
		l+=l&1
		rs=[l,l+1,l+2,l+3]
print reduce(lambda x,y:x^y,rs)
print len(rs)
print ' '.join(map(str,rs))