Leaping Tak

AtCoder

IDabc179_d

Time2000ms

Memory256MB

Difficulty—

There are $N$ cells arranged in a row, numbered $1, 2, \ldots, N$ from left to right. Tak lives in these cells and is currently on Cell $1$. He is trying to reach Cell $N$ by using the procedure described below. You are given an integer $K$ that is less than or equal to $10$, and $K$ non-intersecting segments $[L_1, R_1], [L_2, R_2], \ldots, [L_K, R_K]$. Let $S$ be the union of these $K$ segments. Here, the segment $[l, r]$ denotes the set consisting of all integers $i$ that satisfy $l \leq i \leq r$. * When you are on Cell $i$, pick an integer $d$ from $S$ and move to Cell $i + d$. You cannot move out of the cells. To help Tak, find the number of ways to go to Cell $N$, modulo $998244353$. ## Constraints * $2 \leq N \leq 2 \times 10^5$ * $1 \leq K \leq \min(N, 10)$ * $1 \leq L_i \leq R_i \leq N$ * $[L_i, R_i]$ and $[L_j, R_j]$ do not intersect ($i \neq j$) * All values in input are integers. ## Input Input is given from Standard Input in the following format: $N$ $K$ $L_1$ $R_1$ $L_2$ $R_2$ $:$ $L_K$ $R_K$ [samples]

Samples

Input #1

5 2
1 1
3 4

Output #1

4

The set $S$ is the union of the segment $[1, 1]$ and the segment $[3, 4]$, therefore $S = { 1, 3, 4 }$ holds.
There are $4$ possible ways to get to Cell $5$:

*   $1 \to 2 \to 3 \to 4 \to 5$,
*   $1 \to 2 \to 5$,
*   $1 \to 4 \to 5$ and
*   $1 \to 5$.

Input #2

5 2
3 3
5 5

Output #2

0

Because $S = { 3, 5 }$ holds, you cannot reach to Cell $5$. Print $0$.

Input #3

5 1
1 2

Output #3

Input #4

Output #4

221823067

Note that you have to print the answer modulo $998244353$.

API Response (JSON)

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    "name": "Leaping Tak",
    "description": {
      "content": "There are $N$ cells arranged in a row, numbered $1, 2, \\ldots, N$ from left to right. Tak lives in these cells and is currently on Cell $1$. He is trying to reach Cell $N$ by using the procedure descr",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc179_d"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "There are $N$ cells arranged in a row, numbered $1, 2, \\ldots, N$ from left to right.\nTak lives in these cells and is currently on Cell $1$. He is trying to reach Cell $N$ by using the procedure descr...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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