Occupation

You are given an undirected graph and a starting node $r$. The nodes are numbered $1,2,\dots,N$. To capture node $i$, you must have at least $A_i$ stamina and at least one neighbor of node $i$ must already be captured. After you capture node $i$, your stamina increases by $B_i$. Capturing a node does not decrease your stamina by $A_i$. Find the maximum stamina you can obtain. The start node is already captured, so your stamina at the start is $B_r$.

The first line contains the number of nodes $N$, the number of edges $M$, and the start node $r$, separated by spaces. ($1 \le N \le 500\,000$; $0 \le M \le 1\,000\,000$; $1 \le r \le N$)

The second line contains $A_1, A_2, \dots, A_N$, separated by spaces, the stamina required to capture each node. ($0 \le A_i \le 10^9$; $A_r=0$)

The third line contains $B_1, B_2, \dots, B_N$, separated by spaces, the stamina gained by capturing each node. ($0 \le B_i \le 10^9$)

From the fourth line onward, $M$ lines each contain two integers $u$ and $v$, separated by a space, meaning that $u$ and $v$ are neighbors. ($1 \le u, v \le N$; $u \ne v$)

Print the maximum stamina you can obtain.