Collecting

AtCoder

IDabc214_h

Time4000ms

Memory256MB

Difficulty—

There is a directed graph with $N$ vertices and $M$ edges. The vertices are numbered $1, \dots, N$, and the $i$\-th edge $(1 \leq i \leq M)$ goes from Vertex $A_i$ to Vertex $B_i$. Initially, there are $X_i$ items on Vertex $i$ $(1 \leq i \leq N)$ that someone has lost. $K$ people will collect these items. The $K$ people will travel in the graph one by one. Each person will do the following. * Start on Vertex $1$. Then, traverse an edge any finite number of times. For each vertex visited (including Vertex $1$), collect all items on it if they have not been collected yet. Find the maximum total number of items that can be collected. ## Constraints * $2 \leq N \leq 2 \times 10^5$ * $1 \leq M \leq 2 \times 10^5$ * $1 \leq K \leq 10$ * $1 \leq A_i, B_i \leq N$ * $A_i \neq B_i$ * $A_i \neq A_j$ or $B_i \neq B_j$, if $i \neq j$. * $1 \leq X_i \leq 10^9$ * All values in input are integers. ## Input Input is given from Standard Input in the following format: $N$ $M$ $K$ $A_1$ $B_1$ $\vdots$ $A_M$ $B_M$ $X_1$ $\ldots$ $X_N$ [samples]

Samples

Input #1

Output #1

18

The two people can collect $18$ items as follows.

*   The first person goes $1 \rightarrow 2 \rightarrow 3 \rightarrow 2$ and collects the items on Vertices $1$, $2$, and $3$.
*   The second person goes $1 \rightarrow 5$ and collects the items on Vertex $5$.

It is impossible to collect $19$ or more items, so we should print $18$.

Input #2

3 1 10
2 3
1 100 100

Output #2

API Response (JSON)

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      "content": "There is a directed graph with $N$ vertices and $M$ edges.   The vertices are numbered $1, \\dots, N$, and the $i$\\-th edge $(1 \\leq i \\leq M)$ goes from Vertex $A_i$ to Vertex $B_i$. Initially, there ",
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    "sign": "abc214_h"
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  "statements": [
    {
      "statement_type": "Markdown",
      "content": "There is a directed graph with $N$ vertices and $M$ edges.  \nThe vertices are numbered $1, \\dots, N$, and the $i$\\-th edge $(1 \\leq i \\leq M)$ goes from Vertex $A_i$ to Vertex $B_i$.\nInitially, there ...",
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      "language": "English"
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