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ZOJ Problem Set - 3409
KKV

Time Limit: 10 Seconds      Memory Limit: 65536 KB      Special Judge

KKV (short for Kinetic Kill Vehicle), a new kind of projectile, is a powerful weapon and has a great ability to move in the space. PLA developed a new missile based on the technology of KKV, and this kind of missile can launch and fly in the space, find the target and destroy it.

Now the launch site of the KKV missile is at position (0, 0, 0), the missile will fly through N polygonal lines in order and its initial speed is zero. The initial mass of the missile is M, the mass without fuel is m, and every time the missile can eject some fuel which always has a mass of m0, and the eject speed (scalar) is always v0 (absolute, not relative).

Now give you the N points in order which are the endpoints of the N polygonal lines(The first line is from (0, 0, 0) to the first point, the second line is from the first point to the second point, the third line is from the second point to the third point, etc.), your task is to calculate the time between the KKV missile's launching and its arriving at the Nth point.

The KKV missile is so small that its size can be ignored. It can only and have to eject fuel at all the endpoints except the Nth point, and every time if it ejects fuel, the KKV missile always selects the direction that can make it fly along the next line, and have the largest speed. The motion of the KKV missile obey the principle of momentum conservation, thus m1 × v1 + m2 × v2 = m1 × v'1 + m2 × v'2, here m1 and m2 are the mass of two objects, v1 and v'1 are the original speed and the speed after collision of m1, v2 and v'2 are the original speed and the speed after collision of m2.

But you know that sometimes the PLA will hide some real abilities about their weapons, so sometimes the data might not be valid to this kind of KKV. So, if you find this thing happens, just output "Another kind of KKV.".

Input

There are multiply test cases. Each case begins with a line contains 5 integers N M m m0 and v0, here 1 ≤ N ≤ 40, 1 ≤ m < M - N × m0, M ≤ 200000, 1 ≤ m0, 1 ≤ v0 ≤ 100. Then the following N lines each contains three integers xi yi and zi(1 ≤ iN), indicate the ith point's coordinates. Here -100000 ≤ xi, yi, zi ≤ 100000, and we guarantee that every pair of consecutive lines won't be perpendicular to each other, and the next line won't be in the negative direction of its previous one. (This means three consecutive points cannot be { (0, 0, 0), (0, 0, 3), (1, 1, 2) } or { (0, 0, 0), (0, 0, 3), (1, 1, 3) }, or something like these)

Output

For each test case, output the total flying time of the KKV missile in one line, with two digits after the decimal point, if the data cannot satisfy the KKV missile's flying path, output "Another kind of KKV." instead. If the relative error is no more than 1e-6, the answer will be accepted.

Sample Input

```2 10 1 2 5
2 2 2
4 4 4
2 10 2 2 2
0 0 3
2 2 5
4 10 1 2 20
0 0 40
0 0 80
10 10 110
10 20 115
```

Sample Output

```3.81
10.50
Another kind of KKV.
```

Author: FAN, Yuzhe
Contest: ZOJ Monthly, October 2010
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