Floor Function

Given are integers A, B, and N.

Find the maximum possible value of floor(Ax/B) - A × floor(x/B) for a non-negative integer x not greater than N.

Here floor(t) denotes the greatest integer not greater than the real number t.

Constraints

• 1 ≤ A ≤ 10^{6}
• 1 ≤ B ≤ 10^{12}
• 1 ≤ N ≤ 10^{12}
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

A B N

Output

Print the maximum possible value of floor(Ax/B) - A × floor(x/B) for a non-negative integer x not greater than N, as an integer.

Examples

Input

5 7 4

Output

2

Input

11 10 9

Output

9

inputFormat

input are integers.

Input

Input is given from Standard Input in the following format:

A B N

outputFormat

Output

Print the maximum possible value of floor(Ax/B) - A × floor(x/B) for a non-negative integer x not greater than N, as an integer.

Examples

Input

5 7 4

Output

2

Input

11 10 9

Output

9

样例

5 7 4

2