Sereja has two sequences a and b and number p . Sequence a consists of n integers a 1, a 2, ..., a n . Similarly, sequence b consists of m integers b 1, b 2, ..., b m . As usual, Sereja studies the sequences he has. Today he wants to find the number of positions q (q + (m - 1)·p ≤ n; q ≥ 1), such that sequence b can be obtained from sequence a q , a q + p , a q + 2p , ..., a q + (m - 1)p by rearranging elements. Sereja needs to rush to the gym, so he asked to find all the described positions of q .

输入描述:

The first line contains three integers n, m and p(1 ≤ n, m ≤ 2·105, 1 ≤ p ≤ 2·105). The next line contains n integers a1, a2, ..., an(1 ≤ ai ≤ 109). The next line contains m integers b1, b2, ..., bm(1 ≤ bi ≤ 109).

输出描述:

In the first line print the number of valid qs. In the second line, print the valid values in the increasing order.