Problem

If you bring an empty bottle of $ a $ milk, you can exchange it for a new bottle of $ b $ milk.
How many bottles of milk can Mr. Kawabayashi, who initially has a bottle of $ x $ milk, drink? Output the remainder after dividing by $ 1000000007 $.

Constraints

The input satisfies the following conditions.

• $1 \ leq a \ leq 10 ^ {15}$
• $0 \ leq b \ lt a$
• $0 \ leq x \ leq 10 ^ {15}$

Input

The input is given in the following format.

$ a $ $ b $ $ x $

Three integers $ a $, $ b $, $ x $ are given, separated by spaces.

Output

Print the answer on one line.

Examples

Input

3 1 5

Output

7

Input

3 2 5

Output

11

Input

82 69 64

Output

64

Input

316250877917604 316250877917599 681260158257385

Output

62687552

见题面

见题面