Description

To complete a role-playing game (RPG), you must send your character through N quests. The quests may be passed in any order, but after starting a quest you can’t drop it and switch to another. If your character fails even one quest you fail the whole game. The probability of succeeding in a quest depends on the experience points (XP) of your character at the beginning of the quest, and is determined by the formula
where a_i and b_i are parameters of the i-th quest.
After successful completion of the i-th quest, your character obtains S_i experience points. Initially, it/he/she has D points.

Write a program to determine such an order of the quests that the probability of completing the whole game successfully is the highest possible.

Input

The first line of the input contains the values N (1≤N≤10) and D. Each of the following N lines describes one quest, containing the values a_i, b_i, S_i. The values D, a_i, b_i, S_i (1≤i≤N) are all integers in the range from 0 to 1000 and a_i<b_i (1≤i≤N). Adjacent values on the same line are separated by one or more spaces.

Output

The first line of the output must contain the highest possible probability with the precision of 0.001. The second line must contain the order of quests that ensures this probability. If there are several orders with the same probability, output any one of them.

3 300
350 380 100
100 200 100
440 450 100

1.000
2 1 3

Source

Northeastern Europe 2002, Western Subregion