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Dice Throw


Problem Description

You are given A dices with faces numbered from 1 to B.
You have to find out the number of ways to get to sum C.

Since, the number can be large, output the answer modulo 109 + 7.



Problem Constraints
1 <= A, B, C <= 103


Input Format
The first argument is the integer A.
The second argument is the integer B.
The third argument is the integer C.


Output Format
Return a single integer denoting the number of ways to get to the required sum modulo 109 + 7.


Example Input
Input 1:

A = 2
B = 4
C = 5

Input 2:

A = 2
B = 4
C = 1



Example Output
Output 1:

4

Output 2:

0



Example Explanation
Explanation 1:

There are 4 different ways to arrange the dices - [1, 4], [2, 3], [3, 2], [4, 1].

Explanation 2:

Since, the dices are numbered from 1. 2 dices will have the minimum sum of 2. 
Therefore, there are zero ways to get to sum 1.



NOTE: You only need to implement the given function. Do not read input, instead use the arguments to the function. Do not print the output, instead return values as specified. Still have a question? Checkout Sample Codes for more details.
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