A number of test cases consisting of: A line with an integer 1 ≤ n ≤ 8, the number of people on the tour. A line with an floating point number 1 < v ≤ 100, your maximum speed (you start in the bus at the origin). Then follow n lines, each containing four floating point numbers xi yi vi ai, the starting coordinates (−10⁶ ≤ xi, yi ≤ 10⁶), speed (1 ≤ vi < 100) and direction (0 ≤ ai < 2π) of each of the tour guests. The input is terminated by a case with n = 0, which should not be processed. All floating point numbers in the input will be written in standard decimal notation, and have no more than 10 digits.

For each test case, print a line with the time it takes before everybody is back in the bus (the origin). Round the answer to the nearest integer. The answer will never be larger than 10⁶.

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