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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 links of color links of color links of color , 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 and . Now he would like to buy a new chain, and therefore asks you to write a program to aid him in shopping.
The first line of the standard input gives two integers, and (), 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 integers, (), separated by single spaces. The third line gives integers, (, for ), also separated by single spaces. The sequences and define a nice fragment of a chain - it has to contain exactly links of color . The fourth line gives integers, (), separated by single spaces, that are the colors of successive links of the chain.
In tests worth 50% of total points the constraint holds in addition.
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.
For the input data:
7 3 2 1 1 1 2 3 4 2 1 3 1 2 5
the correct result is:
Explanation of the example: The two nice fragments of this chain are 2, 1, 3, 1 and 1, 3, 1, 2.
Sample grading tests:
Task author: Tomasz Walen.<Submit a solution> [0/100]