P7779 『JROI-2 / Stoi2039』Waiting for You After Class.


Given a positive integer $d$, define $$S_v=\{(x,y):x,y \in \mathbb{Z_{\ge 0}},x^2-dy^2=v\}$$ Compute: $$\sum_{v=1}^{\lfloor\sqrt{d}\rfloor}v[S_v \neq \varnothing]$$ There are multiple queries.

The first line contains a positive integer $t$, which indicates the number of queries. The next $t$ lines each contain a positive integer $d$, representing one query.

For each query, output one line containing one integer, which is the answer.

#### Sample Explanation - For $d=10$, only $v=1$ satisfies $S_v \neq \varnothing$. - For $d=13$, $v=1,3$ satisfy $S_v \neq \varnothing$. - For $d=16$, $v=1,4$ satisfy $S_v \neq \varnothing$. - For $d=19$, $v=1,4$ satisfy $S_v \neq \varnothing$. #### Constraints - For $30\%$ of the testdata, $t=1$, $1 \le d \le 70$. - For $60\%$ of the testdata, $t=1$. - For $100\%$ of the testdata, $1 \le t \le 4 \times 10^3$, $1 \le d \le 2 \times 10^6$. ----- Source: [JROI-2 Summer Fun Round](https://www.luogu.com.cn/contest/30241) - T4. Idea & Solution & Standard & Data: [VinstaG173](/user/59388). Retest: None. Translated by ChatGPT 5