Score : $600$ points
There are $N$ people and $K$ nations, labeled as Person $1$, Person $2$, $\ldots$, Person $N$ and Nation $1$, Nation $2$, $\ldots$, Nation $K$, respectively.
Each person belongs to exactly one nation: Person $i$ belongs to Nation $A_i$.
Additionally, there are $L$ popular people among them: Person $B_1$, Person $B_2$, $\ldots$, Person $B_L$ are popular.
Initially, no two of the $N$ people are friends.
For $M$ pairs of people, Takahashi, a God, can make them friends by paying a certain cost: for each $1\leq i\leq M$, he can pay the cost of $C_i$ to make Person $U_i$ and Person $V_i$ friends.
Now, for each $1\leq i\leq N$, solve the following problem.
Can Takahashi make Person $i$ an indirect friend of a popular person belonging to a nation different from that of Person $i$? If he can do so, find the minimum total cost needed. Here, Person $s$ is said to be an indirect friend of Person $t$ when there exists a non-negative integer $n$ and a sequence of people $(u_0, u_1, \ldots, u_n)$ such that $u_0=s$, $u_n=t$, and Person $u_i$ and Person $u_{i+1}$ are friends for each $0\leq i < n$.
Input is given from Standard Input in the following format:
$N$ $M$ $K$ $L$ $A_1$ $A_2$ $\cdots$ $A_N$ $B_1$ $B_2$ $\cdots$ $B_L$ $U_1$ $V_1$ $C_1$ $U_2$ $V_2$ $C_2$ $\vdots$ $U_M$ $V_M$ $C_M$
Let $X_i$ defined as follows: $X_i$ is $-1$ if it is impossible to make Person $i$ an indirect friend of a popular person belonging to a nation different from that of Person $i$; otherwise, $X_i$ is the minimum total cost needed to do so. Print $X_1, X_2, \ldots, X_N$ in one line, with spaces in between.
4 4 2 2 1 1 2 2 2 3 1 2 15 2 3 30 3 4 40 1 4 10
45 30 30 25
Person $1$, $2$, $3$, $4$ belong to Nation $1$, $1$, $2$, $2$, respectively, and there are two popular people: Person $2$ and $3$. Here,
3 1 3 1 1 2 3 1 1 2 1000000000
-1 1000000000 -1
Note that, for Person $1$, Person $1$ itself is indeed an indirect friend, but it does not belong to a different nation, so there is no popular person belonging to a different nation.