Gold Balanced Lineup

Farmer John's $N$ cows ($1 \le N \le 100{,}000$) share many traits. FJ has narrowed those traits down to a list of only $K$ distinct features ($1 \le K \le 30$). For example, cows with feature #1 might have spots, cows with feature #2 might prefer C over Pascal, and so on.

Each cow is described by a feature ID: a single $K$-bit integer whose binary representation encodes exactly which features the cow has. Reading the binary digits from right (least significant) to left, a $1$ in the $2^{i-1}$ place means the cow exhibits feature $i$. For example, a feature ID of $13$ is $1101$ in binary, so that cow exhibits features $1$, $3$, and $4$, but not feature $2$.

FJ lines the cows up in a row as cows $1 \dots N$ and notices that some contiguous ranges are balanced. A contiguous range of cows $i \dots j$ is balanced when every one of the $K$ features is exhibited by the same number of cows inside that range. Determine the size (number of cows) of the largest balanced range.

• Line $1$: two space-separated integers $N$ and $K$.
• Lines $2 \dots N+1$: line $i+1$ contains a single $K$-bit integer, the feature ID of cow $i$. Its least-significant bit is $1$ if the cow exhibits feature #1, and its most-significant bit is $1$ if the cow exhibits feature #$K$.

• A single integer: the number of cows in the largest contiguous balanced range. If no non-empty range is balanced, output $0$.

The row has $7$ cows with $3$ features. The table below shows the correspondence:

             Feature 3:   1   1   1   0   0   1   0
             Feature 2:   1   1   1   1   0   0   1
             Feature 1:   1   0   1   0   1   0   0
             Key:         7   6   7   2   1   4   2
             Cow #:       1   2   3   4   5   6   7

In the range from cow #3 to cow #6 (size $4$), each feature is exhibited by exactly $2$ cows:

             Feature 3:     1   0   0   1  -> two total
             Feature 2:     1   1   0   0  -> two total
             Feature 1:     1   0   1   0  -> two total
             Key:           7   2   1   4
             Cow #:         3   4   5   6