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: Time Limit Exceeded)

package main

import (
        "fmt"
        "math"
)

func solution(a, b, n int) int {
        ans := -1 << 31

        for i := 1; i <= n; i++ {
                ans = max(ans, int(math.Floor(float64(a)*float64(i)/float64(b))-float64(a)*math.Floor(float64(i)/float64(b))))
        }
        return ans
}

func max(x, y int) int {
        if x > y {
                return x

        }
        return y
}

func main() {
        var a, b, n int
        fmt.Scan(&a, &b, &n)
        fmt.Println(solution(a, b, n))
}