Problem:
Score : 400 points

Problem Statement

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.

Sample Input 1

5 7 4

Sample Output 1

2

When x=3, floor(Ax/B)-A×floor(x/B) = floor(15/7) - 5×floor(3/7) = 2. This is the maximum value possible.

Sample Input 2

11 10 9

Sample Output 2

9

Solution in Go (1.14.1) (judge verdict: Accepted)

package main

import (
	"fmt"
)

func main() {
	var a, b, n int
	fmt.Scanf("%d %d %d", &a, &b, &n)
	answer := maxFloor(a, b, n)
	fmt.Println(answer)
}

func maxFloor(a, b, n int) int {
	m := min(b-1, n)
	return floor(a, b, m)
}

func floor(a, b, x int) int {
	s := a * x / b
	t := a * (x / b)
	return s - t
}

func min(x, y int) int {
	if x < y {
		return x
	}
	return y
}