Pay or Receive

AtCoder

IDabc280_f

Time2000ms

Memory256MB

Difficulty—

There are $N$ towns numbered $1,\ldots,N$ and $M$ roads numbered $1,\ldots,M$. Road $i$ connects towns $A_i$ and $B_i$. When you use a road, your **score** changes as follows: * when you move from town $A_i$ to town $B_i$ using road $i$, your score increases by $C_i$; when you move from town $B_i$ to town $A_i$ using road $i$, your score decreases by $C_i$. Your score may become negative. Answer the following $Q$ questions. * If you start traveling from town $X_i$ with initial score $0$, find the maximum possible score when you are at town $Y_i$. Here, if you cannot get from town $X_i$ to town $Y_i$, print `nan` instead; if you can have as large a score as you want when you are at town $Y_i$, print `inf` instead. ## Constraints * $2\leq N \leq 10^5$ * $0\leq M \leq 10^5$ * $1\leq Q \leq 10^5$ * $1\leq A_i,B_i,X_i,Y_i \leq N$ * $0\leq C_i \leq 10^9$ * All values in the input are integers. ## Input The input is given from Standard Input in the following format: $N$ $M$ $Q$ $A_1$ $B_1$ $C_1$ $\vdots$ $A_M$ $B_M$ $C_M$ $X_1$ $Y_1$ $\vdots$ $X_Q$ $Y_Q$ [samples]

Samples

Input #1

Output #1

\-2
inf
nan

For the first question, if you use road $5$ to move from town $5$ to town $3$, you can have a score $-2$ when you are at town $3$.  
Since you cannot make the score larger, the answer is $-2$.
For the second question, you can have as large a score as you want when you are at town $2$ if you travel as follows: repeatedly "use road $2$ to move from town $1$ to town $2$ and then use road $1$ to move from town $2$ to town $1$" as many times as you want, and finally use road $2$ to move from town $1$ to town $2$.
For the third question, you cannot get from town $3$ to town $1$.

Input #2

2 1 1
1 1 1
1 1

Output #2

inf

The endpoints of a road may be the same, and so may the endpoints given in a question.

Input #3

Output #3

inf
nan
nan
inf
-9

API Response (JSON)

{
  "problem": {
    "name": "Pay or Receive",
    "description": {
      "content": "There are $N$ towns numbered $1,\\ldots,N$ and $M$ roads numbered $1,\\ldots,M$. Road $i$ connects towns $A_i$ and $B_i$. When you use a road, your **score** changes as follows: *   when you move from ",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc280_f"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "There are $N$ towns numbered $1,\\ldots,N$ and $M$ roads numbered $1,\\ldots,M$.\nRoad $i$ connects towns $A_i$ and $B_i$. When you use a road, your **score** changes as follows:\n\n*   when you move from ...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments