# Problem D

Peningar

Languages
en
is
Tómas has found himself in a strange world. This world consists of $n$ cells arranged in a circle. Thus cells $i$ and $i+1$ are adjacent for $1 \leq i < n$, and cells $1$ and $N$ are also adjacent. In each cell there is an $a_ i$ amount of money. Tómas starts at cell $1$. In each step he moves $d$ cells. When landing in a cell Tómas takes all the money in that cell. Can you find out how much money Tómas will get if he continues walking forward until he can’t gather any more money?

## Input

The first line of the input contains two integers
$n,d$ ($1 \leq n \leq 10^5$, $1 \leq d \leq 10^{14}$), where
$n$ is the number of cells
and $d$ is how many cells
Tómas moves forward with each step.

The next line contains $n$ integers, $a_ i$ ($1 \leq a_ i \leq 10^9$), denoting how
much money is in the $i$-th cell.

## Output

Print a single integer, how much money Tómas will end up with.

## Scoring

Group |
Points |
Constraints |

1 |
25 |
$1 \leq n, a_ i \leq 100$, $d = 1$ |

2 |
25 |
$1 \leq n, d, a_ i \leq 100$ |

3 |
50 |
No further constraints |

Sample Input 1 | Sample Output 1 |
---|---|

4 1 1 1 1 1 |
4 |

Sample Input 2 | Sample Output 2 |
---|---|

4 2 1 5 3 5 |
4 |

Sample Input 3 | Sample Output 3 |
---|---|

5 3 1 2 3 4 5 |
15 |