Sum of Abs 2

AtCoder

IDarc178_c

Time2000ms

Memory256MB

Difficulty—

You are given positive integers $N$ and $L$, and a sequence of positive integers $A = (A_{1}, A_{2}, \dots , A_{N})$ of length $N$. For each $i = 1, 2, \dots , N$, answer the following question: > Determine if there exists a sequence of $L$ non-negative integers $B = (B_{1}, B_{2}, \dots, B_{L})$ such that $\displaystyle \sum_{j = 1} ^ {L - 1} \sum_{k = j + 1} ^ {L} |B_{j} - B_{k}| = A_{i}$. If it exists, find the minimum value of $\max(B)$ for such a sequence $B$. ## Constraints * $1 \leq N \leq 2 \times 10^{5}$ * $2 \leq L \leq 2 \times 10^{5}$ * $1 \leq A_{i} \leq 2 \times 10^{5}$ * All input values are integers. ## Input The input is given from Standard Input in the following format: $N$ $L$ $A_{1}$ $A_{2}$ $\cdots$ $A_{N}$ [samples]

Samples

Input #1

2 4
10 5

Output #1

3
-1

For $A_{1} = 10$, if we take $B = (1, 0, 2, 3)$, then $\displaystyle \sum_{j = 1} ^ {L - 1} \sum_{k = j + 1} ^ {L} |B_{j} - B_{k}| = 10$, where $\max(B) = 3$. No non-negative integer sequence $B$ satisfies the condition with $\max(B) < 3$, so print $3$ in the first line.
For $A_{2} = 5$, there is no non-negative integer sequence $B$ that satisfies the condition, so print `-1` in the second line.

Input #2

6 8
167 924 167167 167924 116677 154308

Output #2

API Response (JSON)

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      "statement_type": "Markdown",
      "content": "You are given positive integers $N$ and $L$, and a sequence of positive integers $A = (A_{1}, A_{2}, \\dots , A_{N})$ of length $N$.\nFor each $i = 1, 2, \\dots , N$, answer the following question:\n\n> De...",
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Full JSON Raw Segments