P8762 [Lanqiao Cup 2021 National ABC] 123

Xiao Lan found an interesting sequence. The first few terms are as follows: $1,1,2,1,2,3,1,2,3,4,\ldots$ Xiao Lan noticed that the first $1$ term of this sequence is the integer $1$. The next $2$ terms are the integers from $1$ to $2$. The next $3$ terms are the integers from $1$ to $3$. The next $4$ terms are the integers from $1$ to $4$, and so on. Xiao Lan wants to know the sum of a consecutive segment in this sequence.

The first line contains an integer $T$, which indicates the number of queries. The next $T$ lines each contain one query. In the $i$-th line, there are two integers $l_{i}$ and $r_{i}$, meaning the query asks for the sum from the $l_{i}$-th number to the $r_{i}$-th number in the sequence.

Output $T$ lines. Each line contains one integer representing the answer to the corresponding query.

For $10\%$ of the testdata, $1 \leq T \leq 30$, $1 \leq l_{i} \leq r_{i} \leq 100$. For $20\%$ of the testdata, $1 \leq T \leq 100$, $1 \leq l_{i} \leq r_{i} \leq 1000$. For $40\%$ of the testdata, $1 \leq T \leq 1000$, $1 \leq l_{i} \leq r_{i} \leq 10^{6}$. For $70\%$ of the testdata, $1 \leq T \leq 10000$, $1 \leq l_{i} \leq r_{i} \leq 10^{9}$. For $80\%$ of the testdata, $1 \leq T \leq 1000$, $1 \leq l_{i} \leq r_{i} \leq 10^{12}$. For $90\%$ of the testdata, $1 \leq T \leq 10000$, $1 \leq l_{i} \leq r_{i} \leq 10^{12}$. For all testdata, $1 \leq T \leq 100000$, $1 \leq l_{i} \leq r_{i} \leq 10^{12}$. Lanqiao Cup 2021 National Contest Group A Problem E (Group B Problem F, Group C Problem F). Translated by ChatGPT 5