## Holiday

Jian-Jia is planning his next holiday in Taiwan. During his holiday, Jian-Jia moves from city to city and visits attractions in the cities.

There are n cities in Taiwan, all located along a single highway. The cities are numbered consecutively from 0 to n − 1. For city i, where 0 < i < n − 1, the adjacent cities are i − 1 and i + 1. The only city adjacent to city 0 is city 1, and the only city adjacent to city n − 1 is city n − 2.

Each city contains some number of attractions. Jian-Jia has d days of holiday and plans to visit as many attractions as possible. Jian-Jia has already selected a city in which to start his holiday. In each day of his holiday, Jian-Jia can either move to an adjacent city, or else visit all the attractions of the city he is staying, but not both. Jian-Jia will never visit the attractions in the same city twice even if he stays in the city multiple times. Please help Jian-Jia plan his holiday so that he visits as many different attractions as possible.

### Example

Suppose Jian-Jia has 7 days of holiday, there are 5 cities (listed in the table below), and he starts from city 2. On the first day Jian-Jia visits the 20 attractions in city 2. On the second day Jian-Jia moves from city 2 to city 3, and on the third day visits the 30 attractions in city 3. Jian-Jia then spends the next three days moving from city 3 to city 0, and visits the 10 attractions in city 0 on the seventh day. The total number of attractions Jian-Jia visits is 20 + 30 + 10 = 60, which is the maximum number of attractions Jian-Jia can visit in 7 days when he starts from city 2.

citynumber of attractions
010
12
220
330
41

dayaction
1visit the attractions in city 2
2move from city 2 to city 3
3visit the attractions in city 3
4move from city 3 to city 2
5move from city 2 to city 1
6move from city 1 to city 0
7visit the attractions in city 0

Please write a program that computes the maximum number of attractions Jian-Jia can visit.

### Input Format

Line 1 of input will contain the three integers n, start, and d.
Line 2 of input will contain attraction[0], …, attraction[n-1].

• n: the number of cities.
• start: the index of the starting city.
• d: the number of days.
• attraction: array of length n; attraction[i] is the number of attractions in city i, for 0 ≤ in − 1.

### Output Format

The output should consist of a single integer, the maximum number of attractions Jian-Jia can visit.
Note that the result may be large, and the output value may need to be stored in a 64-bit integer.

5 2 7
10 2 20 30 1

60

### Sample Input 2

100 0 150
4 82 9 38 25 3 48 61 2 39 42 73 64 23 58 42 39 32 34 90 45 12 75 98 90 36 62 97 86 89 69 56 70 44 94 95 47 7 22 16 46 64 89 77 53 46 18 92 45 18 48 56 30 89 20 86 24 48 83 76 36 17 31 72 62 91 32 75 98 54 91 10 85 80 87 37 92 71 96 2 89 9 59 86 98 79 71 21 26 19 63 28 37 94 100 65 50 31 39 13

4436

sample-3.in

334588796671

sample-4.in

### Sample Output 4

3389595012736

In all subtasks 0 ≤ d ≤ 2n + ⌊n/2⌋, and the number of attractions in each city is nonnegative.

subtask% of pointsnmaximum number of attractions in a citystarting city
172 ≤ n ≤ 201,000,000,000no constraints
2232 ≤ n ≤ 100,000100city 0
3172 ≤ n ≤ 3,0001,000,000,000no constraints
4532 ≤ n ≤ 100,0001,000,000,000no constraints

Point Value: 30 (partial)
Time Limit: 5.00s
Memory Limit: 64M
Added: Jul 29, 2014

Languages Allowed:
C++03, PAS, C, HASK, ASM, RUBY, PYTH2, JAVA, PHP, SCM, CAML, PERL, C#, C++11, PYTH3