F. Unusual Sum

Codeforces

IDCF10079F

Time1000ms

Memory256MB

Difficulty—

English · Original

Formal · Original

Bob is an aspiring archaeologist. He has found n ancient scrolls, each with an unusual sum written on it. The sum on the i-th scroll reads as Bob thinks that precise values of these sums encode the location of Aldoredo, the not-so-famous city of gold. Help him calculate the values of the sums! The first line contains a single integer n, the number of scrolls (1 ≤ n ≤ 105). The i-th of the next n lines contains two space-separated integer numbers li and ri, the description of the sum on the i-th scroll (1 ≤ li ≤ ri ≤ 1018). Output n lines: in the i-th line output the value of the sum written on the i-th scroll. Your answer will be considered correct if its relative or absolute error doesn't exceed 10 - 9. ## Input The first line contains a single integer n, the number of scrolls (1 ≤ n ≤ 105). The i-th of the next n lines contains two space-separated integer numbers li and ri, the description of the sum on the i-th scroll (1 ≤ li ≤ ri ≤ 1018). ## Output Output n lines: in the i-th line output the value of the sum written on the i-th scroll. Your answer will be considered correct if its relative or absolute error doesn't exceed 10 - 9. [samples]

**Definitions** Let $ n \in \mathbb{Z} $ be the number of scrolls. For each scroll $ i \in \{1, \dots, n\} $, let $ l_i, r_i \in \mathbb{Z} $ denote the bounds of the sum, with $ 1 \leq l_i \leq r_i \leq 10^{18} $. **Constraints** 1. $ 1 \leq n \leq 10^5 $ 2. For each $ i \in \{1, \dots, n\} $: $ 1 \leq l_i \leq r_i \leq 10^{18} $ **Objective** For each scroll $ i $, compute the sum: $$ S_i = \sum_{k=l_i}^{r_i} k $$ which simplifies to: $$ S_i = \frac{(r_i - l_i + 1)(l_i + r_i)}{2} $$

API Response (JSON)

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