RPG battles 

In many typical RPG games, you battle with bad guys, creatures, monsters or ghosts etc. all the time. After each battle, you may get magic potions that power you up, so you'll get stronger and stronger, and finally defeat the big boss. In this problem, we only consider two kinds of potion: stronger and double power. If you drink a bottle of stronger potion, your power increases by 1; if you drink a bottle of double power potion, your power doubles.

How long each battle lasts depends on how powerful you are. Each battle is described by six parameters: p1, p2, t1, t2, w1, w2. That means, if your power is less than p1, you will be defeated; if your power is greater than p2, you'll need t2 seconds to defeat all the enemies. If your power is between p1 and p2 (inclusive), the time needed for the battle decreases linearly from t1 to t2. For example, if p1 = 50, p2 = 75, t1 = 40, t2 = 15, and your power is 55, then the battle lasts for 35 seconds. Note that the time needed for battles may be non-integers. The last two parameters, w1 and w2, represent the number of bottles of stronger potion and double power potion you got after winning the battle. Note that you don't have to drink these potions immediately. You can drink them later if that'll decrease the total time. You cannot drink potions during a battle, so the time needed for battles is not affected by the potions.

Given the list of battles, your task is to find a strategy to win all the battles as quickly as possible. Note that you must enter the battles in order. You cannot redo or skip any battle.

Input 

There will be at most 25 test cases. Each test begins with two integers n and p ( 1$ \le$n$ \le$1000, 1$ \le$p$ \le$100), the number of battles and your initial power. Each of the next n lines contains 6 integers p1, p2, t1, t2, w1, w2 ( 1$ \le$p1 < p2$ \le$100, 1$ \le$t2 < t1$ \le$100, 0$ \le$w1, w2$ \le$10). The input is terminated by a test case with n = p = 0, you should not process it.

Output 

For each test case, print the shortest time (in seconds) to win all the battles, to two digits after the decimal point. If you cannot win all the battles, print ``Impossible" (without quotes).

Sample Input  

1 55
50 75 40 15 10 0
2 55
50 75 40 15 10 0
50 75 40 15 10 0
3 1
1 2 2 1 0 5
1 2 2 1 1 0
1 100 100 1 0 0
1 7
4 15 35 23 0 0
1 1
2 3 2 1 0 0
0 0

Sample Output  

35.00
60.00
41.00
31.73
Impossible


The Seventh Hunan Collegiate Programming Contest
Problemsetter: Rujia Liu, Special Thanks: Yiming Li & Jane Alam Jan