You are given a sequence $A=(A_0,A_1,\ldots,A_{N-1})$ of length $N$.  
There is an initially empty dish. Takahashi is going to repeat the following operation $K$ times.

-   Let $X$ be the number of candies on the dish. He puts $A_{(X\bmod N)}$ more candies on the dish. Here, $X\bmod N$ denotes the remainder when $X$ is divided by $N$.

Find how many candies are on the dish after the $K$ operations.

Input is given from Standard Input in the following format:

```
$N$ $K$
$A_0$ $A_1$ $\ldots$ $A_{N-1}$
```

Print the answer.

-   $2 \leq N \leq 2\times 10^5$
-   $1 \leq K \leq 10^{12}$
-   $1 \leq A_i\leq 10^6$
-   All values in input are integers.

11

The number of candies on the dish transitions as follows.

• In the 1-st operation, we have X=0, so $A_{(0\ \bmod\ {5})=A_0=2$ more candies will be put on the dish.
• In the 2-nd operation, we have X=2, so $A_{(2\ \bmod\ {5})=A_2=6$ more candies will be put on the dish.
• In the 3-rd operation, we have X=8, so $A_{(8\ \bmod\ {5})=A_3=3$ more candies will be put on the dish.

Thus, after the 3 operations, there will be 11 candies on the dish. Note that you must not print the remainder divided by N.