Given two strings $A$ and $B$, count the number of different ways to choose $k$ non-overlapping consecutive substrings from $A$ to concatenate and form the string $B$. The chosen substrings must maintain their relative order.
### Input
- The first line contains an integer $n,m,k$.
- The second line contains the string $A$ of length $n$.
- The third line contains the string $B$ of length $m$.
### Output
- A single integer representing the number of different ways to choose $k$ non-overlapping consecutive substrings from $A$ to form the string $B$, modulo $10^9+7$.
### Constraints
- $1 \le |A| \le 1000$
- $1 \le |B| \le 200$
- $1 \le k \le |B|$
### Example
Input:
```
6 3 2
aabaab
aab
```
Output:
```
7
```
