Treasure Hunt

Phoenix finally has a treasure map. Phoenix takes the map into a labyrinth full of treasure.

According to the map, the labyrinth has $N$ rooms and $M$ one-way passages, each connecting two rooms. The rooms are numbered 1 to $N$, and room $i$ holds treasure worth $b_i$. You can enter the labyrinth at room 1. With an escape kit, you can leave from any room. However, once you escape, the labyrinth collapses and you cannot go back in to look for more treasure.

Room $a$ has a hidden lever. When you go to room $a$ and pull it, a hidden two-way passage appears between rooms $x$ and $y$.

Phoenix wants to carry out treasure whose total value is as large as possible. What is the maximum total value of treasure Phoenix can collect?

The first line contains the number of rooms $N$ and the number of one-way passages $M$, separated by a space. ($1 \le N \le 100\ 000$, $1 \le M \le 300\ 000$)

The second line contains $N$ integers $b_1, b_2, \ldots, b_N$, separated by spaces, giving the value of the treasure in each room. ($0 \le b_i \le 10^9$)

From the third line onward, the next $M$ lines each contain two integers $u_i$ and $v_i$, separated by a space, giving the start room and the end room of a one-way passage. ($1 \le u_i, v_i \le N$, $u_i \neq v_i$)

For any two different rooms $p$ and $q$, there is at most one one-way passage that starts at $p$ and ends at $q$. ($1 \le p, q \le N$, $p \neq q$)

Line $M+3$ contains the room $a$ with the lever and the two ends $x$ and $y$ of the two-way passage that appears when the lever is pulled, separated by spaces. A one-way passage from room $x$ to room $y$, or from room $y$ to room $x$, may already exist. ($1 \le a, x, y \le N$, $x \neq y$)

Print the maximum total value of treasure that can be collected in one expedition.