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:
import itertools
def solve1(l,r,k):
    p = range(l,r+1)
    ans = l
    ans_p = []
    for i in xrange(2,k+1):
        t = list(itertools.combinations(p,i))
        temp = map(lambda x: reduce(lambda a,b : a ^ b,x),t)
        m = min(temp)
        if m < ans :
            ans = m
            ans_p = [x for x in t[temp.index(m)]]
    if ans_p == []:
        ans_p = [l]
    return ans,ans_p

def solve2(l,r,k):
    if k == 1:   return l,[l]
    if k == 2:
        if l%2 != 0:
            l +=1
        return 1,[l,l+1]
    if k == 3:
        mn = 1
        mx = 3
        while(mx <= r):
            if mn >= l:
                return 0,[mn,mx-1,mx]
            mn *= 2
            mn += 1
            mx *= 2
        return solve2(l,r,2)
    if k == 4:
        if l % 2 != 0:
            return solve2(l+1,r,4)
        else:
            return 0,[l,l+1,l+2,l+3]
    if k > 4:
        if l%2 != 0:
            l+=1
        return 0,[l,l+1,l+2,l+3]
        

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

ans = 0
ans_p = []

if r-l <= 4:
    ans,ans_p = solve1(l,r,k)
else :
    ans,ans_p =solve2(l,r,k)

print ans
print len(ans_p)
print ' '.join(map(str,ans_p))