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E. k-d-sequence

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputWe'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*.

Examples

Input

6 1 2

4 3 2 8 6 2

Output

3 5

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.

Codeforces (c) Copyright 2010-2022 Mike Mirzayanov

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