Best Division

You are given an array $A$ of $N$ integers.

You are also given two integers $K$ and $L$.

You must divide the whole array $A$ into exactly $K$ nonempty intervals so that the length of each interval is at most $L$.

The cost of an interval $[S, E]$ is the bitwise XOR sum of all elements of $A$ whose indices lie in $[S, E]$.

The score of a division is the maximum of the costs of all $K$ intervals in that division. You care about the best division, the one that minimizes the score. That would be too simple, so the problem is reversed.

Suppose you know the minimum score: the answer to the original problem is at most $X$. Now find the maximum value of $K$.

The first line contains three integers $N$, $X$, and $L$ as described above ($1 \le L \le N \le 10^5$, $0 \le X < 268\,435\,456$).

The next line contains three integers $A_{1}$, $P$, and $Q$ ($0 \le A_{1}, P, Q < 268\,435\,456$). The remaining elements of the array $A$ are generated from these three integers as follows: for every $1 < k \le N$, $A_{k} = (A_{k - 1} \cdot P + Q) \bmod 268\,435\,456$.

Print the answer on a single line. If the answer does not exist, print $0$.