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 $*a*_{*q*}, *a*_{*q* + *p*}, *a*_{*q* + 2*p*}, ..., *a*_{*q* + (*m* - 1)*p*}$ by rearranging elements.

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

Input

The first line contains three integers $*n*$, $*m*$ and $*p*$ $(1 ≤ *n*, *m* ≤ 2·10^{5}, 1 ≤ *p* ≤ 2·10^{5})$. The next line contains $*n*$ integers $*a*_{1}$, $*a*_{2}$, $...$, $*a*_{*n*}$ $(1 ≤ *a*_{*i*} ≤ 10^{9})$. The next line contains $*m*$ integers $*b*_{1}$, $*b*_{2}$, $...$, $*b*_{*m*}$ $(1 ≤ *b*_{*i*} ≤ 10^{9})$.

Output

In the first line print the number of valid $*q*$s. In the second line, print the valid values in the increasing order.