Problem Statement

315-san and 8128-san love cream puffs, so the two of them are going to play the cream puff game.
The cream puff game is played using vertices arranged in a circle. There are $N$ vertices, numbered from $1$ to $N$. Vertex $i\ (1 \le i \le N - 1)$ and vertex $i+1$ are adjacent. Vertex $N$ and vertex $1$ are also adjacent. No other pairs of vertices are adjacent. On vertex $i\ (1 \le i \le N)$, $A_i$ cream puffs are placed. Initially, no vertex is occupied.

The game proceeds as follows.

First, 315-san occupies vertex $s$ and eats all the cream puffs placed there. Then, 8128-san occupies vertex $t$ and eats all the cream puffs placed there.
Next, starting with 315-san, the two players alternately perform the following operation until every vertex is occupied by one of them.

• Choose one vertex that is not yet occupied by either player and is adjacent to a vertex occupied by the player, and occupy it
• Eat all the cream puffs placed on the vertex just occupied

Input

$N$
$s\ t$
$A_1\ A_2\ \cdots A_N$

$4\le N\le 10^5$
$1\le s,\ t\le N$
$s\neq t$
$1\le A_i\le 10^9\ (1\le i\le N)$
All inputs are integers.

Output

Output the answer on one line. Print a newline at the end.

Sample

4
1 3
10 20 50 100

40

7
1 7
10 20 30 40 50 60 70

-80