Decrement

AtCoder

IDagc054_f

Time2000ms

Memory256MB

Difficulty—

Given is a sequence $A$ of $N$ positive integers and a sequence $B$ of $N-1$ positive integers. You can do the following operation any number of times. * Choose integers $i$ and $j$ ($1 \leq i < j \leq N$) and decrease each of the following values by $1$: $A_i,A_j,B_i,B_{i+1},\cdots,B_{j-1}$. Here, there should not be any negative value after this operation. Let $m$ be the maximum number of operations that can be done. Find the number, modulo $998244353$, of sequences that $A$ can be after $m$ operations. ## Constraints * $1 \leq N \leq 2 \times 10^5$ * $1 \leq A_i \leq 10^9$ * $1 \leq B_i \leq 10^9$ * All values in input are integers. ## Input Input is given from Standard Input in the following format: $N$ $A_1$ $A_2$ $\cdots$ $A_N$ $B_1$ $B_2$ $\cdots$ $B_{N-1}$ [samples]

Samples

Input #1

3
1 2 2
1 2

Output #1

3

We have $m=2$. After two operations, $A$ will be one of the following three sequences.

*   $A=(1,0,0)$: we end up with this after operations with $(i,j)=(2,3)$ and $(i,j)=(2,3)$.
*   $A=(0,1,0)$: we end up with this after operations with $(i,j)=(1,3)$ and $(i,j)=(2,3)$.
*   $A=(0,0,1)$: we end up with this after operations with $(i,j)=(1,2)$ and $(i,j)=(2,3)$.

Input #2

4
1 1 1 1
2 2 2

Output #2

1

Note that we do not distinguish two scenarios with different contents of $B$ if the contents of $A$ are the same.

Input #3

4
2 2 3 4
3 1 4

Output #3

API Response (JSON)

{
  "problem": {
    "name": "Decrement",
    "description": {
      "content": "Given is a sequence $A$ of $N$ positive integers and a sequence $B$ of $N-1$ positive integers. You can do the following operation any number of times. *   Choose integers $i$ and $j$ ($1 \\leq i < j ",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "agc054_f"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "Given is a sequence $A$ of $N$ positive integers and a sequence $B$ of $N-1$ positive integers. You can do the following operation any number of times.\n\n*   Choose integers $i$ and $j$ ($1 \\leq i < j ...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments