onu

There are n journalists in a hotel in the UN controlled zone, and they are identified by numbers 1, 2, ..., n.
When checking in at the hotel each journalist receives an ID card with a code on it (a positive integer of no more than 10 digits).
The governor of the region wants to go visit the surroundings. Because the number of journalists that want to go with him is too big he decides to draft up a list with groups of journalists in the hotel and he would pick one of them (to his liking). He makes up these group of journalists depending on a non-zero digit k. The following rules are respected for forming the groups:
a) All groups contain the same number of journalists (let's write it down as h).
b) If the journalists of a group have identification numbers x₁, x₂, ..., x_h, (x₁< x₂< ...<x_h) then any two codes c_i , c_i+1 corresponding to identification numbers x_i, x_i+1 (1<=i<h) have the property that the sequence comprised of the last k digits of c_i coincides with the sequence of the first k digits in c_i+1.
c) The number of h journalists in a group is selected so that it be the maximum while meeting property b).

Tasks

Write a program that determines all the groups of journalists that meet above conditions.

Input Data

Input file onu.in contains on the first line two positive integers n and k separated by a space, and on the second line the journalists' codes in ascending ID number order 1, 2, …, n, each separated by a space.

Output Data

Output file onu.out will contain on the first line the number G representing the number of groups that meet task properties and each of the following G lines will contain a group of journalists. Journalists in a group will be written in ascending ID number order. Groups will be written in the file in ascending order.

Constraints and Statements

• 0 < n <= 100
• 0 < k <= 8
• The length of the journalist codes is equal to or greater than k.

Time limit: 2 seconds/test

prof. Doru Popescu Anastasiu
"Radu Greceanu" Slatina National High School
Contact:dopopan@yahoo.com