Codeforces 176B Word Cut (Count DP)

Word CutTime limit:2000MS Memory Limit:262144KB 64bit IO Format:%i64d &%i6 4u SubmitStatusPracticecodeforces 176B

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 a 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 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 .

Ways is considered different if the sequences of applied operations differ. Operation sequences is 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 c11>i-th operation of the second sequence the word splits into parts a and b, a nd additionally x ≠ a holds.

Input

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

The third line contains integer k (0≤ k ≤10^{5)-the required number of operations.< /c14>}

Output

Print a single number-the answer to the problem. As this number can be rather large, print it modulo 1000000007(^{9 + 7).}

Sample Input

Input

Ab
Ab
2

Output

1

Input

Ababab
Ababab
1

Output

2

Input

Ab
Ba
2

Output

0

Hint

The sought-in-the-first sample is:

AB → a|b → ba → b|a → ab

In the second sample the sought ways is:

• Ababab → Abab|ab → ababab
• Ababab → Ab|abab → ababab

"Test Instructions":

Divide a string:w = xy into u = yx(whole order changed, content unchanged)

Ask how many ways, so that just after the K-time division, from the original string into a destination string.

"Problem-solving ideas":

Compare the typical count DP.

Transfer process: (after I divide, how many ways to this string)

Start: Number of original string = 1; other string mode = 0

First: The original string =0 (because it cannot become itself); other =1 (from the original string from the beginning)

Second time: The original string =n-1 (all other strings can be changed back); other =n-2 (except the other + original strings)

......

The DP state should be divided by the number of times K and start point I

But using a scrolling array can divide the number of times

Codeforces 176B Word Cut (Count DP)