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E. Concatenation with intersection
time limit per test
2 seconds
memory limit per test
512 megabytes
input
standard input
output
standard output

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 [l1,r1] (1l1r1n) and a segment [l2,r2] (1l2r2n), and after concatenation he obtains a string a[l1,r1]+b[l2,r2]=al1al1+1ar1bl2bl2+1br2.

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

  • segments [l1,r1] and [l2,r2] have non-empty intersection, i.e. there exists at least one integer x, such that l1xr1 and l2xr2;
  • the string a[l1,r1]+b[l2,r2] is equal to the string s.
Input

The first line contains integers n and m (1n500000,2m2n) — 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.

Examples
Input
6 5
aabbaa
baaaab
aaaaa
Output
4
Input
5 4
azaza
zazaz
azaz
Output
11
Input
9 12
abcabcabc
xyzxyzxyz
abcabcayzxyz
Output
2
Note

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

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