Amulets

AtCoder

IDabc314_g

Time2000ms

Memory256MB

Difficulty—

There are $N$ monsters in a cave: monster $1$, monster $2$, $\ldots$, monster $N$. Each monster has a positive integer **attack power** and a **type** represented by an integer between $1$ and $M$, inclusive. Specifically, for $i = 1, 2, \ldots, N$, the attack power and type of monster $i$ are $A_i$ and $B_i$, respectively. Takahashi will go on an adventure in this cave with a **health** of $H$ and some of the $M$ amulets: amulet $1$, amulet $2$, $\ldots$, amulet $M$. In the adventure, Takahashi performs the following steps for $i = 1, 2, \ldots, N$ in this order (as long as his health does not drop to $0$ or below). * If Takahashi has not brought amulet $B_i$ with him, monster $i$ will attack him and decrease his health by $A_i$. * Then, * if his health is greater than $0$, he defeats monster $i$; * otherwise, he dies without defeating monster $i$ and ends his adventure. Solve the following problem for each $K = 0, 1, \ldots, M$ independently. > Find the maximum number of monsters that Takahashi can defeat when choosing $K$ of the $M$ amulets to bring on the adventure. The constraints guarantee that there is at least one monster of type $i$ for each $i = 1, 2, \ldots, M$. ## Constraints * $1 \leq M \leq N \leq 3 \times 10^5$ * $1 \leq H \leq 10^9$ * $1 \leq A_i \leq 10^9$ * $1 \leq B_i \leq M$ * For each $1 \leq i \leq M$, there is $1 \leq j \leq N$ such that $B_j = i$. * All input values are integers. ## Input The input is given from Standard Input in the following format: $N$ $M$ $H$ $A_1$ $B_1$ $A_2$ $B_2$ $\vdots$ $A_N$ $B_N$ [samples]

Samples

Input #1

Output #1

2 5 7 7

Consider the case $K = 1$. Here, Takahashi can bring amulet $2$ to defeat the maximum possible number of monsters, which is $5$. The adventure proceeds as follows.

*   For $i = 1$, he avoids the attack of monster $1$ since he has amulet $2$. Then, he defeats monster $1$.
*   For $i = 2$, he takes the attack of monster $2$ and his health becomes $6$ since he does not have amulet $1$. Then, he defeats monster $2$.
*   For $i = 3$, he avoids the attack of monster $3$ since he has amulet $2$. Then, he defeats monster $3$.
*   For $i = 4$, he avoids the attack of monster $4$ since he has amulet $2$. Then, he defeats monster $4$.
*   For $i = 5$, he takes the attack of monster $5$ and his health becomes $1$ since he does not have amulet $1$. Then, he defeats monster $5$.
*   For $i = 6$, he takes the attack of monster $6$ and his health becomes $-8$ since he does not have amulet $3$. Then, he dies without defeating monster $6$ and ends his adventure.

Similarly, when $K=0$, he can defeat $2$ monsters; when $K=2$, he can defeat all $7$ monsters by bringing amulets $2$ and $3$; when $K=3$, he can defeat all $7$ monsters by bringing amulets $1$, $2$, and $3$.

Input #2

Output #2

8 12 15 15 15 15

API Response (JSON)

{
  "problem": {
    "name": "Amulets",
    "description": {
      "content": "There are $N$ monsters in a cave: monster $1$, monster $2$, $\\ldots$, monster $N$. Each monster has a positive integer **attack power** and a **type** represented by an integer between $1$ and $M$, in",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc314_g"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "There are $N$ monsters in a cave: monster $1$, monster $2$, $\\ldots$, monster $N$. Each monster has a positive integer **attack power** and a **type** represented by an integer between $1$ and $M$, in...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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