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 Kotlin (1.3.71) (judge verdict: Time Limit Exceeded)

fun main(args: Array<String>) = ABC165D.main()

object ABC165D {
    fun log(message: Any?) {
        println(message)// TODO: ←消す
    }

    val A: Int
    val B: Long
    val N: Long

    init {
        val (a, b, n) = readLongs()
        A = a.toInt()
        B = b
        N = n
    }

    fun main() {
        //val ans = (1..N).map { x ->
        //    A * x / B - A * floorDiv(x,B)
        //}.max()

        val scores = (0..N / B - 1).asSequence().map { floor ->
            val x = (floor + 1) * B - 1
            A * x / B - A * floor
        } + sequenceOf(A * N / B - A * (N / B))

        val ans = scores.max()

        println(ans)
    }

    /*####################################################################################*/

    fun readLongs() = readLine()!!.split(" ").map { it.toLong() }
}