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: Accepted)

#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef vector<long long> vll;
typedef vector<pair<int, int>> vpi;
typedef vector<pair<long long, long long>> vpl;
typedef pair<int, int> pii;
typedef pair<long long, long long> pll;
#define INF (int)(1e9)
#define MAXX 1.1529215e+18
#define inf 999999
#define EPS (1e-7)
#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 FOR(i, k, n) for (int i = (k); i < (int)(n); i++)
#define ALL(a) a.begin(), a.end()
#define RALL(a) a.begin(), a.end(), greater<int>()
#define ROT(a) a.begin(), a.begin() + 1, a.end()
#define RROT(a) a.begin(), a.end() - 1, a.end()
#define PB push_back
#define MP make_pair
#define PI acos(-1.0)
#define sz(a) a.size()
const ll MOD = 1e9 + 7;
const int MAX = 10000000;
template <typename T1, typename T2>
inline bool chmin(T1& a, T2 b)
{
    if (a > b) {
        a = b;
        return 1;
    }
    return 0;
}
template <typename T1, typename T2>
inline bool chmax(T1& a, T2 b)
{
    if (a < b) {
        a = b;
        return 1;
    }
    return 0;
}
template <typename T>
T gcd(T a, T b)
{
    if (b == 0)
        return a;
    return gcd(b, a % b);
}
//cout << 'H' << endl;
/*--------------------------------------------*/

int main()
{
    //cout << fixed << setprecision(10)
    cin.tie(0);
    ios::sync_with_stdio(false);

    ll A, B, N;
    cin >> A >> B >> N;

    ll ans = 0;

    ll l = 1, r = min(B, N);


    if (N < B) {
        cout << (A * N) / B << endl;
    } else {
        cout << (A * (B - 1)) / B << endl;
    }
}