A very friendly group
In a class, there are N girls and M boys. The class teacher, Snizhana Denysivna, needs to select a group consisting of L girls and K boys for a class presentation. This group must be very friendly, meaning that each selected boy must be friends with each selected girl. Snizhana Denysivna wants to know all the possible ways to form such a friendly group, so she can choose the best one from her perspective. Your task is to help her by calculating the total number of ways to form this very friendly group of children. Since the result can be very large, provide the answer modulo 1000000007.
Input
The first line of the input file contains the natural numbers N, M, L, K. Here, L ≤ N ≤ 100000 and K ≤ M ≤ 15. The next N lines each contain M characters, either 0 or 1. The j-th character of the i-th line is 1 if and only if the i-th girl is friends with the j-th boy.
Output
Output the solution to the problem on a single line of the output file.