P7281 [COCI 2020/2021 #4] Vepar

Given two sets of positive integers $\{a,a+1,\cdots,b\}$ and $\{c,c+1,\cdots,d\}$, determine whether $c \cdot (c+1)\cdots d$ is divisible by $a \cdot (a+1)\cdots b$.

The first line contains an integer $t$, which indicates the number of test cases. In the next $t$ lines, four integers $a_i,b_i,c_i,d_i$ are given.

Output $t$ lines in total. For the $i$-th line, if $c_i \cdot (c_i+1)\cdots d_i$ is divisible by $a_i \cdot (a_i+1)\cdots b_i$, output `DA`; otherwise, output `NE`.

#### Explanation for Sample 1 According to the statement, multiplying the numbers gives $9 \times 10=90$ and $3 \times 4 \times 5 \times 6=360$. Since $90$ is divisible by $360$, output `DA`. We get $2 \times 3 \times 4 \times 5=120$ and $7 \times 8 \times 9=504$. Since $120$ is not divisible by $504$, output `NE`. #### Constraints and Specifications This problem **does not use bundled evaluation**. You can get the corresponding score by passing the corresponding subtasks, but there are several constraints. | Constraint ID | Score | Constraints and Specifications | | :----------: | :----------: | :----------: | | $1$ | $10$ | $a_i,b_i,c_i,d_i \le 50$ | | $2$ | $20$ | $a_i,b_i,c_i,d_i \le 1000$ | | $3$ | $10$ | $a_i=1$ | | $4$ | $30$ | None | For $100\%$ of the testdata, $1 \le t \le 10$, $1 \le a_i \le b_i \le 10^7$, $1 \le c_i \le d_i \le 10^7$. #### Notes **The score of this problem follows the original COCI settings, with a full score of $70$.** **Translated from [COCI2020-2021](https://hsin.hr/coci/) [CONTEST #4](https://hsin.hr/coci/contest4_tasks.pdf) _T2 Vepar_.** Translated by ChatGPT 5