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 (
	"bufio"
	"fmt"
	"math"
	"os"
	"strconv"
)

var sc = bufio.NewScanner(os.Stdin)

const initBufSize, maxBufSize = 10000, 1000000

func nextStr() string {
	sc.Scan()
	return sc.Text()
}

func nextInt() int {
	sc.Scan()
	i, e := strconv.Atoi(sc.Text())
	if e != nil {
		panic(e)
	}
	return i
}

func nextInts(n int) []int {
	res := make([]int, n)
	for i := range res {
		res[i] = nextInt()
	}
	return res
}

func min(nums ...int) int {
	if len(nums) == 0 {
		panic("funciton min() requires at least one argument.")
	}
	res := nums[0]
	for i := 0; i < len(nums); i++ {
		res = int(math.Min(float64(res), float64(nums[i])))
	}
	return res
}

func max(nums ...int) int {
	if len(nums) == 0 {
		panic("funciton max() requires at least one argument.")
	}
	res := nums[0]
	for i := 0; i < len(nums); i++ {
		res = int(math.Max(float64(res), float64(nums[i])))
	}
	return res
}

func abs(n int) int {
	return int(math.Abs(float64(n)))
}

func pow(r, n int) int {
	return int(math.Pow(float64(r), float64(n)))
}

func calc(a, b, x int) int {
	va, vb, vx := float64(a), float64(b), float64(x)
	return int(math.Floor(va*vx/vb) - (va * math.Floor(vx/vb)))
}

func main() {
	sc.Split(bufio.ScanWords)
	sc.Buffer(make([]byte, initBufSize), maxBufSize)
	a := nextInt()
	b := nextInt()
	n := nextInt()
	if n < b {
		fmt.Println(calc(a, b, n))
	} else {
		fmt.Println(calc(a, b, b-1))
	}
}