Not Too Many Balls

AtCoder

IDabc332_g

Time3000ms

Memory256MB

Difficulty—

There are several balls. Each ball is one of the colors $1$, $2$, $\ldots$, $N$, and for each $i = 1, 2, \ldots, N$, there are $A_i$ balls of color $i$. Additionally, there are $M$ boxes. For each $j = 1, 2, \ldots, M$, the $j$\-th box can hold up to $B_j$ balls in total. Here, for all pairs of integers $(i, j)$ satisfying $1 \leq i \leq N$ and $1 \leq j \leq M$, the $j$\-th box may hold at most $(i \times j)$ balls of color $i$. Print the maximum total number of balls that the $M$ boxes can hold. ## Constraints * All input values are integers. * $1 \leq N \leq 500$ * $1 \leq M \leq 5 \times 10^5$ * $0 \leq A_i, B_i \leq 10^{12}$ ## Input The input is given from Standard Input in the following format: $N$ $M$ $A_1$ $A_2$ $\ldots$ $A_N$ $B_1$ $B_2$ $\ldots$ $B_M$ [samples]

Samples

Input #1

2 3
8 10
4 3 8

Output #1

14

You can do as follows to put a total of $14$ balls into the boxes while satisfying the conditions in the problem statement.

*   For balls of color $1$, put one into the first box, one into the second box, and three into the third box.
*   For balls of color $2$, put two into the first box, two into the second box, and five into the third box.

Input #2

1 1
1000000000000
0

Output #2

Input #3

10 12
59 168 130 414 187 236 330 422 31 407
495 218 351 105 351 414 198 230 345 297 489 212

Output #3

API Response (JSON)

{
  "problem": {
    "name": "Not Too Many Balls",
    "description": {
      "content": "There are several balls. Each ball is one of the colors $1$, $2$, $\\ldots$, $N$, and for each $i = 1, 2, \\ldots, N$, there are $A_i$ balls of color $i$. Additionally, there are $M$ boxes. For each $j ",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 3000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc332_g"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "There are several balls. Each ball is one of the colors $1$, $2$, $\\ldots$, $N$, and for each $i = 1, 2, \\ldots, N$, there are $A_i$ balls of color $i$.\nAdditionally, there are $M$ boxes. For each $j ...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments