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 ≤ 2·10⁵; 0 ≤ k ≤ 2·10⁵; 0 ≤ d ≤ 10⁹). The second line contains n space-separated integers: a₁, a₂, ..., a_n ( - 10⁹ ≤ a_i ≤ 10⁹) — 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.

k-d-sequence

Examples