The province of Bali has many sculptures located on its roads. Let's focus on one of its main roads.
There are sculptures on that main road, conveniently numbered
through
consecutively. The age of sculpture
is
years. To make the road more beautiful, the government wants to partition the sculptures into several groups. Then, the government will plant beautiful trees between the groups, to attract more tourists to Bali.
Here is the rule in partitioning the sculptures:
- The sculptures must be partitioned into exactly
groups, where
. Each group must consist of at least one sculpture. Each sculpture must belong to exactly one group. The sculptures in each group must be consecutive sculptures on the road.
- For each group, compute the sum of the ages of the sculptures in that group.
- Finally, compute the bitwise OR of the above sums. Let's call this the final beauty value of the partition.
What is the minimum final beauty value that the government can achieve?
Note: the bitwise OR of two non-negative integers and
is computed as follows:
- Convert
and
into binary.
- Let
= number of bits of
, and
= number of bits of
. Let
.
- Represent
in binary as
and
in binary as
, where
and
are the
th bits of
and
, respectively. The (
)st bits are the most significant bits, while the
th bits are the least significant bits.
, in binary, is defined as
, where
Input Specification
The first line contains three space-separated integers ,
, and
. The second line contains
space-separated integers
.
Output Specification
A single line containing the minimum final beauty value.
Sample Input
6 1 3
8 1 2 1 5 4
Sample Output
11
Explanation of Sample Output
Partition the sculptures into 2 groups: and
. The sums are
and
. The final beauty value is
.
Comments
Can we partition the sculptures into only one group?
If
, sure. But won't that always give you the maximum beauty value?