Little Bytie loves to play with colorful chains. He already has quite an impressive collection, and some of them he likes more than the others. Each chain consists of a certain number of colorful links. Byteasar has noticed that Bytie's sense of aesthetics is very precise. It turns out that Bytie finds a contiguous fragment of a chain nice if it contains exactly l₁ links of color c₁,l₂ links of color c₂,…,l_m links of color c_m, and moreover it contains no links of other colors. A chain's appeal is its number of (contiguous) fragments that are nice. By trial and error, Byteasar has determined the values c₁,…,c_m and l_m,…,l_m. Now he would like to buy a new chain, and therefore asks you to write a program to aid him in shopping.

입력 형식

The first line of the standard input gives two integers, n and m (1 ≤ m ≤ n ≤ 1,000,000), separated by a single space. These are the length of the chain and the length of a nice fragment's description. The second line gives m integers, l₁,…,l_m (1 ≤ l_i ≤ n), separated by single spaces. The third line gives m integers, c₁,…,c_m (1 ≤ c_i ≤ n, c_i≠c_j for i≠j), also separated by single spaces. The sequences l₁,…,l_m and c₁,…,c_m define a nice fragment of a chain - it has to contain exactly l_i links of color c_i. The fourth line gives n integers, a₁,…,a_n(1 ≤ a_i ≤ n), separated by single spaces, that are the colors of successive links of the chain.</p>

출력 형식

Your program is to print a single integer, the number of nice contiguous fragments in the chain, to the first and only line of the standard output.

예제 입력

7 3
2 1 1
1 2 3
4 2 1 3 1 2 5

예제 출력

2

힌트

The two nice fragments of this chain are 2, 1, 3, 1 and 1, 3, 1, 2.