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D. Little Victor and Set

time limit per test

1 secondmemory limit per test

256 megabytesinput

standard inputoutput

standard outputLittle 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*the following inequality holds*l*≤*x*≤*r*; - 1 ≤ |
*S*| ≤*k*; - lets denote the
*i*-th element of the set*S*as*s*_{i}; value 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* ≤ 10^{12}; 1 ≤ *k* ≤ *min*(10^{6}, *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 represents the operation of bitwise exclusive OR. In other words, it is the XOR operation.

Codeforces (c) Copyright 2010-2022 Mike Mirzayanov

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