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 <algorithm>
#include <array>
#include <cmath>
#include <cstdlib>
#include <deque>
#include <functional>
#include <iomanip>
#include <iostream>
#include <queue>
#include <sstream>
#include <stack>
#include <string>
#include <tuple>
#include <unordered_map>
#include <unordered_set>
#include <vector>

#define REP(X, Y, Z) for (ll(X) = (Y); (X) < (Z); (X)++)

using namespace std;
using ll = long long;
using dll = deque<ll>;
using pll = pair<ll, ll>;
using qll = queue<ll>;
using usll = unordered_set<ll>;
using umll = unordered_map<ll, ll>;
using sll = stack<int>;
using vll = vector<ll>;
using vvll = vector<vll>;

constexpr ll kMod = 1e9 + 7;

ll gcd(ll a, ll b) {
  if (a < b) {
    return gcd(b, a);
  }
  ll c = a % b;
  while (c != 0) {
    a = b;
    b = c;
    c = a % b;
  }
  return b;
}

ll lcm(ll a, ll b) {
  return a / gcd(a, b) * b;
}

void init() {
  cin.tie(nullptr);
  ios_base::sync_with_stdio(false);
  cout << fixed << setprecision(15);
}

int main() {
  init();

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

  ll max = 0;
  ll c = 1;
  for (ll i = N; i >= 0; i -= c) {
    ll ans = (A * i / B) - A * (i / B);
    if (max < ans) { max = ans; }
    if (c < A) { c += c; }
  }
  cout << max << endl;

  return 0;
}