Problem Statement

Snuke has a sequence of $N$ integers $a=(a_1,a_2,\cdots,a_N)$ consisting of $0$s and $1$s, and an empty integer sequence $b$. The initial state $a_i=S_i$ is given to you as input.

Snuke can do the following three operations any number of times in any order.

• Shift $a$ to the right. In other words, replace $a$ with $(a_N,a_1,a_2,\cdots,a_{N-1})$.
• Shift $a$ to the left. In other words, replace $a$ with $(a_2,a_3,\cdots,a_N,a_1)$.
• Append the current value of $a_1$ at the end of $b$.

You are also given a sequence of $M$ integers $T=(T_1,T_2,\cdots,T_M)$. Determine whether it is possible to make $b$ equal to $T$. If it is possible, find the minimum number of operations needed to do so.

Constraints

• $1 \leq N \leq 2 \times 10^5$
• $1 \leq M \leq 2 \times 10^5$
• $0 \leq S_i \leq 1$
• $0 \leq T_i \leq 1$
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

N M
S_1 S_2 \cdots S_N
T_1 T_2 \cdots T_M

Output

If it is impossible to make $b$ equal to $T$, print -1. If it is possible, print the minimum number of operations needed to do so.