Sereja has two sequences a and b and number p. Sequence a consists of n integers a1,a2,...,an. Similarly, sequence b consists of m integers b1,b2,...,bm. As usual, Sereja studies the sequences he has. Today he wants to find the number of positions q (q+(m-1) \cdot p \le n;q \ge 1), such that sequence b can be obtained from sequence aq,aq+p,aq+2p,...,aq+(m-1)p by rearranging elements.

Sereja needs to rush to the gym, so he asked to find all the described positions of q.

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

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