Warp

AtCoder

IDabc265_e

Time3000ms

Memory256MB

Difficulty—

Takahashi is at the origin of a two-dimensional plane. Takahashi will repeat teleporting $N$ times. In each teleportation, he makes one of the following moves: * Move from the current coordinates $(x,y)$ to $(x+A,y+B)$ * Move from the current coordinates $(x,y)$ to $(x+C,y+D)$ * Move from the current coordinates $(x,y)$ to $(x+E,y+F)$ There are obstacles on $M$ points $(X_1,Y_1),\ldots,(X_M,Y_M)$ on the plane; he cannot teleport to these coordinates. How many paths are there resulting from the $N$ teleportations? Find the count modulo $998244353$. ## Constraints * $1 \leq N \leq 300$ * $0 \leq M \leq 10^5$ * $-10^9 \leq A,B,C,D,E,F \leq 10^9$ * $(A,B)$, $(C,D)$, and $(E,F)$ are distinct. * $-10^9 \leq X_i,Y_i \leq 10^9$ * $(X_i,Y_i)\neq(0,0)$ * $(X_i,Y_i)$ are distinct. * All values in input are integers. ## Input Input is given from Standard Input in the following format: $N$ $M$ $A$ $B$ $C$ $D$ $E$ $F$ $X_1$ $Y_1$ $X_2$ $Y_2$ $\vdots$ $X_M$ $Y_M$ [samples]

Samples

Input #1

2 2
1 1 1 2 1 3
1 2
2 2

Output #1

5

The following $5$ paths are possible:

*   $(0,0)\to(1,1)\to(2,3)$
*   $(0,0)\to(1,1)\to(2,4)$
*   $(0,0)\to(1,3)\to(2,4)$
*   $(0,0)\to(1,3)\to(2,5)$
*   $(0,0)\to(1,3)\to(2,6)$

Input #2

10 3
-1000000000 -1000000000 1000000000 1000000000 -1000000000 1000000000
-1000000000 -1000000000
1000000000 1000000000
-1000000000 1000000000

Output #2

Input #3

300 0
0 0 1 0 0 1

Output #3

292172978

API Response (JSON)

{
  "problem": {
    "name": "Warp",
    "description": {
      "content": "Takahashi is at the origin of a two-dimensional plane.   Takahashi will repeat teleporting $N$ times. In each teleportation, he makes one of the following moves: *   Move from the current coordinates",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 3000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc265_e"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "Takahashi is at the origin of a two-dimensional plane.  \nTakahashi will repeat teleporting $N$ times. In each teleportation, he makes one of the following moves:\n\n*   Move from the current coordinates...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments