We'll call a sequence of integers a good *k*-*d* sequence if we can add to it at most *k* numbers in such a way that after the sorting the sequence will be an arithmetic progression with difference *d*.

You got hold of some sequence *a*, consisting of *n* integers. Your task is to find its longest contiguous subsegment, such that it is a good *k*-*d* sequence.
The first line contains three space-separated integers *n*, *k*, *d* (1 ≤ *n* ≤ 2·10<sup class="upper-index">5</sup>; 0 ≤ *k* ≤ 2·10<sup class="upper-index">5</sup>; 0 ≤ *d* ≤ 10<sup class="upper-index">9</sup>). The second line contains *n* space-separated integers: *a*<sub class="lower-index">1</sub>, *a*<sub class="lower-index">2</sub>, ..., *a*<sub class="lower-index">*n*</sub> ( - 10<sup class="upper-index">9</sup> ≤ *a*<sub class="lower-index">*i*</sub> ≤ 10<sup class="upper-index">9</sup>) — the actual sequence.
print("_RANDOM_GUESS_1689177318.329071")# 1689177318.3290849