Small d and k

AtCoder

IDabc254_e

Time3500ms

Memory256MB

Difficulty—

We have a simple undirected graph with $N$ vertices and $M$ edges. The vertices are numbered $1,\ldots,N$. For each $i=1,\ldots,M$, the $i$\-th edge connects Vertex $a_i$ and Vertex $b_i$. Additionally, **the degree of each vertex is at most $3$.** For each $i=1,\ldots,Q$, answer the following query. * Find the sum of indices of vertices whose distances from Vertex $x_i$ are at most $k_i$. ## Constraints * $1 \leq N \leq 1.5 \times 10^5$ * $0 \leq M \leq \min (\frac{N(N-1)}{2},\frac{3N}{2})$ * $1 \leq a_i \lt b_i \leq N$ * $(a_i,b_i) \neq (a_j,b_j)$, if $i\neq j$. * The degree of each vertex in the graph is at most $3$. * $1 \leq Q \leq 1.5 \times 10^5$ * $1 \leq x_i \leq N$ * $0 \leq k_i \leq 3$ * All values in input are integers. ## Input Input is given from Standard Input in the following format: $N$ $M$ $a_1$ $b_1$ $\vdots$ $a_M$ $b_M$ $Q$ $x_1$ $k_1$ $\vdots$ $x_Q$ $k_Q$ [samples]

Samples

Input #1

Output #1

1
20
2
20
7
6
20

For the $1$\-st query, the only vertex whose distance from Vertex $1$ is at most $1$ is Vertex $1$, so the answer is $1$.  
For the $2$\-nd query, the vertices whose distances from Vertex $2$ are at most $2$ are Vertex $2$, $3$, $4$, $5$, and $6$, so the answer is their sum, $20$.  
The $3$\-rd and subsequent queries can be answered similarly.

API Response (JSON)

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  "problem": {
    "name": "Small d and k",
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      "content": "We have a simple undirected graph with $N$ vertices and $M$ edges. The vertices are numbered $1,\\ldots,N$. For each $i=1,\\ldots,M$, the $i$\\-th edge connects Vertex $a_i$ and Vertex $b_i$. Additionall",
      "description_type": "Markdown"
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    "platform": "AtCoder",
    "limit": {
      "time_limit": 3500,
      "memory_limit": 262144
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    "difficulty": "None",
    "is_remote": true,
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    "sync_url": null,
    "sign": "abc254_e"
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  "statements": [
    {
      "statement_type": "Markdown",
      "content": "We have a simple undirected graph with $N$ vertices and $M$ edges. The vertices are numbered $1,\\ldots,N$. For each $i=1,\\ldots,M$, the $i$\\-th edge connects Vertex $a_i$ and Vertex $b_i$. Additionall...",
      "is_translate": false,
      "language": "English"
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}

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