Fountain Flow Matching Pairs

In this problem, you are given historical records on water flow indices from six different fountain regions over $N$ years. In the $i$-th year, the water flow indices for the six regions are represented by $A_{i,1}, A_{i,2}, \dots, A_{i,6}$ (each index is a non-negative integer less than $2^{30}$).

Your task is to count the number of pairs of different years $(i, j)$ (with $i < j$) such that exactly $K$ fountain regions have the same water flow index in both years. In other words, you need to count the number of pairs $(i, j)$ satisfying:

[ \sum_{r=1}^{6} \mathbf{1}(A_{i,r} = A_{j,r}) = K, ]

where (\mathbf{1}(\cdot)) is the indicator function that is 1 when the condition is true and 0 otherwise.

Note: It is guaranteed that the 6 values in each record pertain to distinct fountain regions.

inputFormat

The first line contains two integers $N$ and $K$, where $N$ is the number of years, and $K$ is the exact number of regions that must match between two years.

Then follow $N$ lines, each containing 6 space-separated non-negative integers: $A_{i,1}, A_{i,2}, \dots, A_{i,6}$.

outputFormat

Output a single integer, the number of pairs $(i, j)$ (with $i < j$) that satisfy the condition that exactly $K$ fountain regions have the same water flow indexes.

sample

3 2
1 2 3 4 5 6
1 2 7 8 9 10
1 3 3 4 5 11

1