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 PYTHON3):

Solution:
from functools import reduce

xor = lambda x, y: x ^ y

l, r, k = map(int, input().split())
result = []
if r - l < 5:
    result = [l]
    l1 = [([], list(range(l, r + 1)))]
    l2 = []
    for i in range(1, k + 1):
        for test, trash in l1:
            for j, el in enumerate(trash):
                l2.append((test + [el], trash[:j] + trash[j + 1:]))
        for test, trash in l2:
            if reduce(xor, test) < reduce(xor, result):
                result = test
        l1 = l2
        l2 = []
else:
    if k == 1:
        result = [l]
    elif k == 2:
        x = l + l % 2
        result = [x, x + 1]
    elif k == 3:
        i = 1
        while 3 * 2 ** (i - 1) <= r:
            if (2 ** i - 1 >= l):
                result = [2 ** i - 1, 3 * 2 ** (i - 1) - 1, 3 * 2 ** (i - 1)]
                break
            i += 1
        if not result:
            x = l + l % 2
            result = [x, x + 1]
    else:
        x = l + l % 2
        result = [x, x + 1, x + 2, x + 3]
print(reduce(xor, result))
print(len(result))
print(" ".join(map(str, result)))