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.

Input

The first line contains three space-separated integers $*n*, *k*, *d*$ ($1 ≤ *n* ≤ 2·10^{5}; 0 ≤ *k* ≤ 2·10^{5}; 0 ≤ *d* ≤ 10^{9}$). The second line contains $*n*$ space-separated integers: $*a*_{1}, *a*_{2}, ..., *a*_{*n*}$ ($- 10^{9} ≤ *a*_{*i*} ≤ 10^{9}$) — the actual sequence.

Output

Print two space-separated integers $*l*, *r*$ ($1 ≤ *l* ≤ *r* ≤ *n*$) show that sequence $*a*_{*l*}, *a*_{*l* + 1}, ..., *a*_{*r*}$ is the longest subsegment that is a good $*k*$-$*d*$ sequence.

If there are multiple optimal answers, print the one with the minimum value of $*l*$.

Note

In the first test sample the answer is the subsegment consisting of numbers 2, 8, 6 — after adding number 4 and sorting it becomes sequence 2, 4, 6, 8 — the arithmetic progression with difference 2.