World Tour Finals

AtCoder

IDabc323_c

Time2000ms

Memory256MB

Difficulty—

The programming contest World Tour Finals is underway, where $N$ players are participating, and half of the competition time has passed. There are $M$ problems in this contest, and the score $A_i$ of problem $i$ is a multiple of $100$ between $500$ and $2500$, inclusive. For each $i = 1, \ldots, N$, you are given a string $S_i$ that indicates which problems player $i$ has already solved. $S_i$ is a string of length $M$ consisting of `o` and `x`, where the $j$\-th character of $S_i$ is `o` if player $i$ has already solved problem $j$, and `x` if they have not yet solved it. Here, none of the players have solved all the problems yet. The total score of player $i$ is calculated as the sum of the scores of the problems they have solved, plus a **bonus score** of $i$ points. For each $i = 1, \ldots, N$, answer the following question. * At least how many of the problems that player $i$ has not yet solved must player $i$ solve to exceed all other players' current total scores? Note that under the conditions in this statement and the constraints, it can be proved that player $i$ can exceed all other players' current total scores by solving all the problems, so the answer is always defined. ## Constraints * $2\leq N\leq 100$ * $1\leq M\leq 100$ * $500\leq A_i\leq 2500$ * $A_i$ is a multiple of $100$. * $S_i$ is a string of length $M$ consisting of `o` and `x`. * $S_i$ contains at least one `x`. * All numeric values in the input are integers. ## Input The input is given from Standard Input in the following format: $N$ $M$ $A_1$ $A_2$ $\ldots$ $A_M$ $S_1$ $S_2$ $\vdots$ $S_N$ [samples]

Samples

Input #1

3 4
1000 500 700 2000
xxxo
ooxx
oxox

Output #1

0
1
1

The players' total scores at the halfway point of the competition time are $2001$ points for player $1$, $1502$ points for player $2$, and $1703$ points for player $3$.
Player $1$ is already ahead of all other players' total scores without solving any more problems.
Player $2$ can, for example, solve problem $4$ to have a total score of $3502$ points, which would exceed all other players' total scores.
Player $3$ can also, for example, solve problem $4$ to have a total score of $3703$ points, which would exceed all other players' total scores.

Input #2

5 5
1000 1500 2000 2000 2500
xxxxx
oxxxx
xxxxx
oxxxx
oxxxx

Output #2

Input #3

7 8
500 500 500 500 500 500 500 500
xxxxxxxx
oxxxxxxx
ooxxxxxx
oooxxxxx
ooooxxxx
oooooxxx
ooooooxx

Output #3

API Response (JSON)

{
  "problem": {
    "name": "World Tour Finals",
    "description": {
      "content": "The programming contest World Tour Finals is underway, where $N$ players are participating, and half of the competition time has passed. There are $M$ problems in this contest, and the score $A_i$ of ",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc323_c"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "The programming contest World Tour Finals is underway, where $N$ players are participating, and half of the competition time has passed. There are $M$ problems in this contest, and the score $A_i$ of ...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments