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 C++ (GCC 9.2.1) (judge verdict: Wrong Answer)

#include <bits/stdc++.h>
using namespace std;

#pragma GCC target("avx")
#pragma GCC optimize("O3")
#pragma GCC optimize("unroll-loops")

#define rep(i, n) for (int i = 0; i < (int)(n); i++)
#define REP(i, n) for (int i = 1; i <= (int)(n); i++)
#define repi(i, s, n) for (int i = (s); i < (int)(n); i++)
#define all(x) (x).begin(), (x).end()
#define uniqueV(x)            \
    sort(x.begin(), x.end()); \
    x.erase(unique(x.begin(), x.end()), x.end());
#define debug(x) cerr << #x << ": " << x << '\n'
#define debug2(x, y) cerr << "(" << #x << ", " << #y << ") = " \
                          << "(" << x << ", " << y << ")" << '\n'

typedef long long int ll;
typedef pair<int, int> P;

const long long INF = 3e18 + 12;
const int inf = 1e9;

// ----------------------------------------------

ll f(ll a, ll b, ll x)
{
    return int((a * x) / b) - a * int(x / b);
}

int main()
{
    ios::sync_with_stdio(false);
    cin.tie(0);

    ll a, b, n;
    cin >> a >> b >> n;

    ll left = 1, right = n + 1;

    while (right - left > 1)
    {
        long double mid = left + (right - left) / 2;

        if (f(a, b, left) < f(a, b, mid))
            left = mid;
        else
            right = mid;
    }
    cout << setprecision(10) << setiosflags(ios::fixed);
    cout << f(a, b, left) << endl;

    return 0;
}