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:
def f(arr):
    val = 0
    for x in arr:
        val ^= x
    return val
 
 
def solve(l, r, k):
    ret = [l]
    if k >= 2:
        cand = [l, l + 1]
        if f(cand) < f(ret):
            ret = cand
        if l + 2 <= r:
            cand = [l + 1, l + 2]
            if f(cand) < f(ret):
                ret = cand
    if k >= 3:
        x = 1
        while x <= l:
            x *= 2
        if x + x // 2 <= r:
            ret = [x - 1, x + x // 2, x + x // 2 - 1]
    if k >= 4:
        cand = [l, l + 1, l + 2, l + 3]
        if f(cand) < f(ret):
            ret = cand
        if l + 4 <= r:
            cand = [l + 1, l + 2, l + 3, l + 4]
            if f(cand) < f(ret):
                ret = cand
    return ret
 
 
l, r, k = map(int, input().split())
ans = solve(l, r, k)
print(f(ans))
print(len(ans))
print(' '.join(map(str, ans)))