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 cities in Taiwan, all located along a single highway. The cities are numbered consecutively from 0 to . For city , where , the adjacent cities are and . The only city adjacent to city 0 is city 1, and the only city adjacent to city is city .

Each city contains some number of attractions. Jian-Jia has 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 , which is the maximum number of attractions Jian-Jia can visit in 7 days when he starts from city 2.

city | number of attractions |
---|---|

0 | 10 |

1 | 2 |

2 | 20 |

3 | 30 |

4 | 1 |

day | action |
---|---|

1 | visit the attractions in city 2 |

2 | move from city 2 to city 3 |

3 | visit the attractions in city 3 |

4 | move from city 3 to city 2 |

5 | move from city 2 to city 1 |

6 | move from city 1 to city 0 |

7 | visit the attractions in city 0 |

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

#### Input Specification

- Line of input will contain the three integers , start, and .
- Line of input will contain . : the number of cities. start: the index of the starting city. : the number of days. attraction: array of length ; is the number of attractions in city , for .

#### 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 Output 3

`334588796671`

#### Sample Input 4

#### Sample Output 4

`3389595012736`

#### Subtasks

In all subtasks , and the number of attractions in each city is non-negative.

##### Additional constraints:

subtask | points | maximum number of attractions in a city | starting city | |
---|---|---|---|---|

1 | 7 | no constraints | ||

2 | 23 | city 0 | ||

3 | 17 | no constraints | ||

4 | 53 | no constraints |

## Comments