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: Wrong Answer)

package main

import (
	"fmt"
	"math"
)

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

	var score, ans int
	tmp := int(math.Sqrt(float64(b)))

	strt := 0
	if n-tmp-2 > 0 {
		strt = n - tmp - 2
	}

	k := a % b
	for i := strt; i < b; i++ {
		score = a*(i%b) - (k*(i%b))%b
		score /= b
		if ans <= score {
			ans = score
		}

		if i == n {
			break
		}
	}
	fmt.Println(ans)
}