Description

Define the following function

Given the value C of F(p1, p2 ... pn), can you find the minimum and maximum value of F(q1, q2 ... qn)?

Input

The input contains several test cases. For each test case, it contains three lines.

Line 1: two integers n (1<= n <= 50000) and C.

Line 2: n integers p1, p2 ... pn (|pi| < 1000 for 1 <= i <= n).

Line 3: n integers q1, q2 ... qn (|qi| < 1000 for 1 <= i <= n).

Output

For each test case, output the minimum and maximum value in a single line with the fraction rounded to 3 decimal places.

2 1
3 1
0 2

2.000 2.000

Source

POJ Monthly--2005.08.28,Static