Hate Stagnant Water

Jaehyeong likes clean water and hates stagnant water. Today he also visits a village with water tanks to get clean water.

The village has $N$ water tanks. Each tank stores either clean water or stagnant water. The tanks are connected to each other by $M$ pipes for easier supply.

When he visits tank $K$ to get clean water, he can get clean water if, among tank $K$ and the tanks he can reach from tank $K$ through zero or more pipes, the number of tanks with clean water is greater than the number of tanks with stagnant water.

For each visit described in the input, determine whether he can get clean water.

The first line contains the number of tanks $N$ ($1 \leq N \leq 100\,000$), the number of pipes $M$ ($0 \leq M \leq 200\,000$), and the number of visits $Q$ ($1 \leq Q \leq 100\,000$).

The second line contains the type of water in tanks $1$ through $N$, in order. Clean water is given as 1 and stagnant water as 0.

From the 3rd line to the $(M+2)$th line, each line contains two tank numbers $u$ and $v$ ($1 \leq u, v \leq N$, $u \neq v$) connected by a pipe. Multiple pipes may connect the same pair of tanks.

From the $(M+3)$th line to the $(M+Q+2)$th line, each line contains a tank number $K$ ($1 \leq K \leq N$) that Jaehyeong visits.

For each visit, print 1 if he can get clean water at that tank, and 0 otherwise. Print the answers in the order of the input queries, one per line, a total of $Q$ lines.