Colorful Chain

Bytie loves playing with colorful chains. He already owns quite a collection, and he likes some of them more than others. A chain is a row of colored links.

Byteasar has noticed that Bytie's taste is very precise. Bytie calls a contiguous fragment of a chain nice if it contains exactly $l_1$ links of color $c_1$, exactly $l_2$ links of color $c_2$, $\dots$, exactly $l_m$ links of color $c_m$, and no links of any other color. The appeal of a chain is the number of nice contiguous fragments it contains.

After many attempts Byteasar worked out the values $c_1, \dots, c_m$ and $l_1, \dots, l_m$. He now wants to buy a new chain, so he asks you for a program that helps him shop.

The first line contains two integers $n$ and $m$ separated by a single space ($1 \le m \le n \le 1\,000\,000$): the length of the chain and the length of the description of a nice fragment.

The second line contains $m$ integers $l_1, \dots, l_m$ separated by single spaces ($1 \le l_i \le n$).

The third line contains $m$ integers $c_1, \dots, c_m$ separated by single spaces ($1 \le c_i \le n$, and $c_i \ne c_j$ whenever $i \ne j$).

The sequences $l_1, \dots, l_m$ and $c_1, \dots, c_m$ define a nice fragment: it has to contain exactly $l_i$ links of color $c_i$.

The fourth line contains $n$ integers $a_1, \dots, a_n$ separated by single spaces ($1 \le a_i \le n$), the colors of the successive links of the chain.

Print a single integer, the number of nice contiguous fragments in the chain.

In the first example the nice fragments are 2 1 3 1 and 1 3 1 2, so the answer is 2.