Concatenation with intersection

2000ms

524288K

Description:

Vasya had three strings $$$a$$$, $$$b$$$ and $$$s$$$, which consist of lowercase English letters. The lengths of strings $$$a$$$ and $$$b$$$ are equal to $$$n$$$, the length of the string $$$s$$$ is equal to $$$m$$$.

Vasya decided to choose a substring of the string $$$a$$$, then choose a substring of the string $$$b$$$ and concatenate them. Formally, he chooses a segment $$$[l_1, r_1]$$$ ($$$1 \leq l_1 \leq r_1 \leq n$$$) and a segment $$$[l_2, r_2]$$$ ($$$1 \leq l_2 \leq r_2 \leq n$$$), and after concatenation he obtains a string $$$a[l_1, r_1] + b[l_2, r_2] = a_{l_1} a_{l_1 + 1} \ldots a_{r_1} b_{l_2} b_{l_2 + 1} \ldots b_{r_2}$$$.

Now, Vasya is interested in counting number of ways to choose those segments adhering to the following conditions:

segments $$$[l_1, r_1]$$$ and $$$[l_2, r_2]$$$ have non-empty intersection, i.e. there exists at least one integer $$$x$$$, such that $$$l_1 \leq x \leq r_1$$$ and $$$l_2 \leq x \leq r_2$$$;
the string $$$a[l_1, r_1] + b[l_2, r_2]$$$ is equal to the string $$$s$$$.

Input:

The first line contains integers $$$n$$$ and $$$m$$$ ($$$1 \leq n \leq 500\,000, 2 \leq m \leq 2 \cdot n$$$) — the length of strings $$$a$$$ and $$$b$$$ and the length of the string $$$s$$$.

The next three lines contain strings $$$a$$$, $$$b$$$ and $$$s$$$, respectively. The length of the strings $$$a$$$ and $$$b$$$ is $$$n$$$, while the length of the string $$$s$$$ is $$$m$$$.

All strings consist of lowercase English letters.

Output:

Print one integer — the number of ways to choose a pair of segments, which satisfy Vasya's conditions.

Sample Input:

6 5
aabbaa
baaaab
aaaaa

Sample Output:

Sample Input:

5 4
azaza
zazaz
azaz

Sample Output:

Sample Input:

9 12
abcabcabc
xyzxyzxyz
abcabcayzxyz

Sample Output:

Note:

Let's list all the pairs of segments that Vasya could choose in the first example:

$$$[2, 2]$$$ and $$$[2, 5]$$$;
$$$[1, 2]$$$ and $$$[2, 4]$$$;
$$$[5, 5]$$$ and $$$[2, 5]$$$;
$$$[5, 6]$$$ and $$$[3, 5]$$$;

Informação

Provedor Codeforces

Código CF1313E