There are L stations along a circular railway, numbered 1 through L. Trains travel in both directions, and take 1 minute to get from a station to the neighbouring one (i.e., between 1st and 2nd, between 2nd and 3rd,..., between (L-1)-th and L-th and between L-th and 1-st).

There are n employee's houses along the railway, and n offices, each house or office located near a railway station. You are to establish a one-to-one correspondence between houses and offices in such a way that total travel time (sum of travel times of each employee) is minimized.

The first line of the input file contains two integer numbers, n and L (1 ≤ n ≤ 50000, 2 ≤ L ≤ 10⁹). The second line contains n locations of the employee's houses, and the third line contains n locations of the offices. Each location is an integer number between 1 and L. Some houses or offices or both can be located at the same railway station.

Output the minimal total travel time followed by the description of the one-to-one correspondence. The description should be represented by n numbers (one for each employee, ordered as in the input), denoting the 1-based index of the office assigned to the corresponding employee.

sample input	sample output
3 15 1 2 10 11 12 13	9 2 3 1

sample input	sample output
4 12 2 5 8 11 6 9 12 3	4 4 1 2 3