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.

Please compute the maximum number of attractions Jian-Jia can visit.

Input Specification

• Line ~1~ of input will contain the three integers ~n~, start, and ~d~.
• Line ~2~ of input will contain ~attraction[0], \dots, 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 \le i \le n - 1~.

Output Specification

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.

Sample Input 1

5 2 7
10 2 20 30 1

Sample Output 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

Sample Output 2

4436

Sample Input 3

sample-3.in

Sample Output 3

334588796671

Sample Input 4

sample-4.in

Sample Output 4

3389595012736

Subtasks

In all subtasks ~0 \le d \le 2n+\lfloor n/2\rfloor~, and the number of attractions in each city is non-negative.

Additional constraints:

subtask	points	~n~	maximum number of attractions in a city	starting city
1	7	~2 \le n \le 20~	~1\,000\,000\,000~	no constraints
2	23	~2 \le n \le 100\,000~	~100~	city 0
3	17	~2 \le n \le 3\,000~	~1\,000\,000\,000~	no constraints
4	53	~2 \le n \le 100\,000~	~1\,000\,000\,000~	no constraints