Word Cut

2000ms

262144K

Description:

Let's consider one interesting word game. In this game you should transform one word into another through special operations.

Let's say we have word w, let's split this word into two non-empty parts x and y so, that w = xy. A split operation is transforming word w = xy into word u = yx. For example, a split operation can transform word "wordcut" into word "cutword".

You are given two words start and end. Count in how many ways we can transform word start into word end, if we apply exactly k split operations consecutively to word start.

Two ways are considered different if the sequences of applied operations differ. Two operation sequences are different if exists such number i (1 ≤ i ≤ k), that in the i-th operation of the first sequence the word splits into parts x and y, in the i-th operation of the second sequence the word splits into parts a and b, and additionally x ≠ a holds.

Input:

The first line contains a non-empty word start, the second line contains a non-empty word end. The words consist of lowercase Latin letters. The number of letters in word start equals the number of letters in word end and is at least 2 and doesn't exceed 1000 letters.

The third line contains integer k (0 ≤ k ≤ 10⁵) — the required number of operations.

Output:

Print a single number — the answer to the problem. As this number can be rather large, print it modulo 1000000007 (10⁹ + 7).

Sample Input:

ab
ab
2

Sample Output:

Sample Input:

ababab
ababab
1

Sample Output:

Sample Input:

ab
ba
2

Sample Output:

Note:

The sought way in the first sample is:

ab → a|b → ba → b|a → ab

In the second sample the two sought ways are:

ababab → abab|ab → ababab
ababab → ab|abab → ababab

Informação

Provedor Codeforces

Código CF176B