Jubeat

Recently, Nana is spending a lot of time playing “Jubeat”, the latest arcade music game from Konami. The game consists of a $4 \times 4$ grid. When a note pops up in some of the cells, the player must push that cell following the rhythm of the music.

For each note pushed, the player is awarded points. If a song contains $N$ notes, a player will receive $\frac{900\\,000}{N}$ points if the timing of the push is perfect. For notes where the timing was less perfect, she can receive either $70$%, $30$%, or $0$% of this score. After the song is over, the sum of all the points will be rounded down to the nearest integer.

Nana just played a song and received a score of $S$: however he doesn’t know the number of notes $N$ in the song. However, he suspects $N$ lies in an interval $\[a, b]$. Write a program that calculates the sum of all possible $N$s in that range.

The input consists of $T$ test cases. The number of test cases $T$ is given in the first line of the input. Each test case consists of a single line with three integers: $S$ ($0 ≤ S ≤ 900\\,000$), $a$ and $b$ ($1 ≤ a ≤ b ≤ 10^9$).

Print exactly one line for each test case. The line should contain an integer indicating the sum of all possible $N$ in the given range.