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:
def Func(ar):
	ret = 0
	for c in ar:
		ret^=c
	return ret
	
def try_all(ar,k):
	ret = []
	if k >= 2:
		for i in xrange(len(ar)):
			for j in xrange(i+1,len(ar)):
				ret += [ [ar[i],ar[j]] ]	
	if k >= 3:
		for i in xrange(len(ar)):
			ret += [ ar[:i]+ar[i+1:] ]
	if k >=4: 
		ret += [ar]
	return ret
	

l,r,k = map(int,raw_input().split())
ans = [l]

		
if k == 1: ans = [l]



if k >= 2:
	if r-l+1<=4:
		for z in try_all([x for x in range(l,r+1)],k):
			if Func(ans)>Func(z): ans = z
			
	
	tmp = l
	if tmp%2==1: tmp+=1
	b = [l]
	if tmp<r: b = [tmp,tmp+1] 
	if Func(ans)>Func(b): ans = b
if k>=3:
	mn = 1
	mx = 3
	b = [l]
	while mx<=r:
		if mn>=l:
			b = [mn,mx-1,mx]
		mx*=2
		mn*=2
		mn+=1
	if Func(ans)>Func(b): ans = b

if k>=4:
	tt = l
	while tt<=r-3 and tt%2!=0: tt+=1
	if tt%2==0 and tt<=r-3: ans = [tt,tt+1,tt+2,tt+3]
	
print Func(ans)
print len(ans)
print ' '.join(map(str,ans))