Child to Parent

AtCoder

IDagc063_e

Time4000ms

Memory256MB

Difficulty—

There is a rooted tree with $N$ vertices numbered $1$ to $N$. Vertex $1$ is the root, and the parent of vertex $i$ ($2\leq i\leq N$) is $P_i$. You are given a non-negative integer $r$ and a sequence of non-negative integers $A = (A_1, \ldots, A_N)$. You can perform the following operation on the sequence any number of times, possibly zero. * Choose an $i$ such that $i\geq 2$ and $A_i \geq 1$. Replace $A_i$ with $A_i - 1$ and $A_{P_i}$ with $A_{P_i}+r$. Find the number, modulo $998244353$, of possible final states of the sequence $A$. ## Constraints * $2\leq N\leq 300$ * $1\leq P_i \leq i - 1$ ($2\leq i\leq N$) * $0\leq r \leq 10^9$ * $0\leq A_i \leq 10^9$ ## Input The input is given from Standard Input in the following format: $N$ $P_2$ $\ldots$ $P_N$ $r$ $A_1$ $\ldots$ $A_N$ [samples]

Samples

Input #1

Output #1

4

The four possible final states of $A$ are $(1,1,1)$, $(3,0,1)$, $(3,1,0)$, and $(5,0,0)$.

Input #2

Output #2

5

The five possible final states of $A$ are $(1,1,1)$, $(1,2,0)$, $(2,0,1)$, $(2,1,0)$, and $(3,0,0)$.

Input #3

Output #3

6

The six possible final states of $A$ are $(1,1,1)$, $(1,3,0)$, $(3,0,1)$, $(3,2,0)$, $(5,1,0)$, and $(7,0,0)$.

Input #4

Output #4

Input #5

Output #5

87782255

API Response (JSON)

{
  "problem": {
    "name": "Child to Parent",
    "description": {
      "content": "There is a rooted tree with $N$ vertices numbered $1$ to $N$. Vertex $1$ is the root, and the parent of vertex $i$ ($2\\leq i\\leq N$) is $P_i$. You are given a non-negative integer $r$ and a sequence o",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 4000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "agc063_e"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "There is a rooted tree with $N$ vertices numbered $1$ to $N$. Vertex $1$ is the root, and the parent of vertex $i$ ($2\\leq i\\leq N$) is $P_i$.\nYou are given a non-negative integer $r$ and a sequence o...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments