Sum Sum Max

AtCoder

IDabc240_f

Time2000ms

Memory256MB

Difficulty—

There are integer sequences $A, B, C$ of length $M$ each. $C$ is represented by integers $x_1, \dots, x_N, y_1, \dots, y_N$. The first $y_1$ terms of $C$ are $x_1$, the subsequent $y_2$ terms are $x_2$, $\ldots$, the last $y_N$ terms are $x_N$. $B$ is defined by $B_i = \sum_{k = 1}^i C_k \, (1 \leq i \leq M)$. $A$ is defined by $A_i = \sum_{k = 1}^i B_k \, (1 \leq i \leq M)$. Find the maximum value among $A_1, \dots, A_M$. You will be given $T$ test cases to solve. ## Constraints * $1 \leq T \leq 2 \times 10^5$ * $1 \leq N \leq 2 \times 10^5$ * The sum of $N$ in a single file is at most $2 \times 10^5$. * $1 \leq M \leq 10^9$ * $|x_i| \leq 4 \, (1 \leq i \leq N)$ * $y_i \gt 0 \, (1 \leq i \leq N)$ * $\sum_{k = 1}^N y_k = M$ * All values in input are integers. ## Input Input is given from Standard Input in the following format: $T$ $\mathrm{case}_1$ $\vdots$ $\mathrm{case}_T$ Each case is in the following format: $N$ $M$ $x_1$ $y_1$ $\vdots$ $x_N$ $y_N$ [samples]

Samples

Input #1

3
3 7
-1 2
2 3
-3 2
10 472
-4 12
1 29
2 77
-1 86
0 51
3 81
3 17
-2 31
-4 65
4 23
1 1000000000
4 1000000000

Output #1

4
53910
2000000002000000000

In the first test case, we have:

*   $C = (-1, -1, 2, 2, 2, -3, -3)$
*   $B = (-1, -2, 0, 2, 4, 1, -2)$
*   $A = (-1, -3, -3, -1, 3, 4, 2)$

Thus, the maximum value among $A_1, \dots, A_M$ is $4$.

API Response (JSON)

{
  "problem": {
    "name": "Sum Sum Max",
    "description": {
      "content": "There are integer sequences $A, B, C$ of length $M$ each. $C$ is represented by integers $x_1, \\dots, x_N, y_1, \\dots, y_N$. The first $y_1$ terms of $C$ are $x_1$, the subsequent $y_2$ terms are $x_2",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc240_f"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "There are integer sequences $A, B, C$ of length $M$ each.\n$C$ is represented by integers $x_1, \\dots, x_N, y_1, \\dots, y_N$. The first $y_1$ terms of $C$ are $x_1$, the subsequent $y_2$ terms are $x_2...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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