Crushing blow

Khodislav is playing D&D. Right now his character is fighting a monster, and Khodislav, who is for some reason very sure of his attack, wants to finish the enemy with a final crushing blow. His character has several weapons; the damage a weapon can deal is determined by rolling dice and described by three numbers $n$, $f$, and $m$, where $n$ is the number of dice, $f$ is the number of faces on each die, and $m$ is a modifier. For example, if $n = 3$, $f = 8$, $m = 5$, you roll three eight-faced dice, add up the results, and add five to the sum to get the damage; this is usually written as $3d8 + 5$.

To finish the monster, a weapon must deal damage of $D$ or greater. Help Khodislav choose a weapon for his character that kills the monster with maximum probability.

Dice rolls are independent, and every face of a die is equally likely. Each face of a die has one of the numbers from $1$ to $f$ written on it.

The first line of the input file contains a single integer $T$, the number of tests ($1 \le T \le 5\,000$). The descriptions of $T$ tests follow.

The first line of a test contains two integers: $W$, the number of the character's weapons, and $D$, the minimum damage needed to finish the monster ($1 \le W \le 5\,000$, $1 \le D \le 250$).

The next $W$ lines describe the weapons. Each line contains three integers: $n$, the number of dice, $f$, the number of faces on each die, and $m$, the modifier ($1 \le n \le 10$, $2 \le f \le 20$, $-10 \le m \le 10$).

The total number of weapons over all tests does not exceed $5\,000$.

For each test, print on a separate line a single real number: the maximum probability of dealing damage of at least $D$ with one blow. The absolute error of the answers must not exceed $10^{-11}$.