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,...,an (-109≤ai≤109)− the actual sequence.
Output
Print two space-separated integers l,r (1≤l≤r≤n) show that sequence al,al+1,...,ar 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.