#ifdef __LOCAL #define _GLIBCXX_DEBUG #endif #include #include using namespace std; using namespace atcoder; typedef unsigned long long ull; typedef long long ll; const double PI = 3.14159265358979323846; #define rep(i, n) for (ll i = 0; i < (ll)(n); i++) // aよりもbが大きいならばaをbで更新する // (更新されたならばtrueを返す) template bool chmax(T& a, const T& b) { if (a < b) { a = b; // aをbで更新 return true; } return false; } // aよりもbが小さいならばaをbで更新する // (更新されたならばtrueを返す) template bool chmin(T& a, const T& b) { if (a > b) { a = b; // aをbで更新 return true; } return false; } // a^p // 2^3 = 2 * 2^2 // 2^2 = 2 * (2^1) // 2^1 = 2 ll modpow(ll a, ll p, ll mod) { if (p == 0) return 1; a %= mod; if (p % 2 == 0) { ll half = modpow(a, p / 2, mod) % mod; return half * half % mod; } else { return a * modpow(a, p - 1, mod) % mod; } } // a^p ll powpow(ll a, ll p) { if (p == 0) return 1; if (p % 2 == 0) { ll half = pow(a, p / 2); return half * half; } else { return a * pow(a, p - 1); } } // a/b // https://qiita.com/drken/items/3b4fdf0a78e7a138cd9a ll moddiv(ll a, ll b, ll mod) { return a * modpow(b, mod - 2, mod); } // nCa を求める ll modCombination(ll n, ll a, ll mod) { if (n < 0 || a < 0 || n < a) return 0; if (n - a < a) { return modCombination(n, n - a, mod); } ll denominator = 1; // 分母 ll numerator = 1; // 分子 for (ll i = 0; i < a; i++) { denominator *= a - i; numerator *= n - i; denominator %= mod; numerator %= mod; } return numerator * modpow(denominator, mod - 2, mod) % mod; } vector> combination(ll n) { vector> C(n + 1, vector(n + 1)); C[0][0] = 1; rep(i, n) rep(j, i + 1) { C[i + 1][j + 1] += C[i][j]; C[i + 1][j] += C[i][j]; } return C; } // ref. https://drken1215.hatenablog.com/entry/2018/06/08/210000 class ModCombinationTable { private: ll mod; vector fac, finv, inv; public: ModCombinationTable(ll n, ll _mod) : mod(_mod) { fac.resize(n + 1); finv.resize(n + 1); inv.resize(n + 1); fac[0] = fac[1] = 1; finv[0] = finv[1] = 1; inv[1] = 1; for (ll i = 2; i <= n; i++) { fac[i] = fac[i - 1] * i % mod; inv[i] = mod - inv[mod % i] * (mod / i) % mod; finv[i] = finv[i - 1] * inv[i] % mod; } } ll operator()(ll n, ll k) { if (n < k) return 0; if (n < 0 || k < 0) return 0; return fac[n] * (finv[k] * finv[n - k] % mod) % mod; } }; // cf. https://qiita.com/drken/items/a14e9af0ca2d857dad23 vector enum_divisors(ll n) { vector res; // sqrt(n)まで試し割り for (ll i = 1; i * i <= n; i++) { if (n % i == 0) { res.push_back(i); // 重複しないならばiの相方であるn/iも約数 // e.g. n=25のときのi=5は重複 if (n / i != i) res.push_back(n / i); } } sort(res.begin(), res.end()); return res; } // cf. https://qiita.com/drken/items/a14e9af0ca2d857dad23 map prime_factors(ll n) { map res; // sqrt(n)まで試し割り for (ll a = 2; a * a <= n; a++) { if (n % a != 0) continue; // nで割れる限り割る while (n % a == 0) { res[a]++; n /= a; } } if (n != 1) res[n]++; return res; } ll gcd(ll a, ll b) { if (b == 0) return a; else return gcd(b, a % b); } ll lcm(ll a, ll b) { return (a / gcd(a, b)) * b; } // p/q struct fraction { ll p, q; fraction(ll _p = 0, ll _q = 1) : p(_p), q(_q) { if (q == 0) { p = 1; return; } if (q < 0) { p = -p; q = -q; } ll g = gcd(p, q); p /= g; q /= g; } bool operator<(const fraction& other) const { return p * other.q < q * other.p; } bool operator<=(const fraction& other) const { return p * other.q <= q * other.p; } bool operator==(const fraction& other) const { return p == other.p && q == other.q; } }; // res[i][c] := i 文字目以降で最初に文字 c が登場する index (存在しないときは n) vector> calcNext(const string& S) { ll n = (ll)S.size(); vector> res(n + 1, vector(26, n)); for (ll i = n - 1; i >= 0; --i) { for (ll j = 0; j < 26; ++j) res[i][j] = res[i + 1][j]; res[i][S[i] - 'a'] = i; } return res; } // ref. https://algo-logic.info/bridge-lowlink/ struct LowLink { vector> G; vector ord, low; vector visited; vector> bridges; LowLink(const vector>& _G) : G(_G) { visited.resize(G.size(), false); ord.resize(G.size(), 0); low.resize(G.size(), 0); ll k = 0; rep(i, (ll)G.size()) { if (visited[i]) continue; k = dfs(i, k); } } ll dfs(ll node, ll k, ll parent = -1) { visited[node] = true; ord[node] = k; low[node] = k; k++; for (auto g : G[node]) { if (!visited[g]) { k = dfs(g, k, node); low[node] = min(low[node], low[g]); if (ord[node] < low[g]) { bridges.emplace_back(node, g); } } else if (g != parent) { low[node] = min(low[node], ord[g]); } } return k; } }; // 3x3(アフィン変換) struct matrix { vector> a; matrix(const vector>& _a = {{1, 0, 0}, {0, 1, 0}, {0, 0, 1}}) : a(_a) {} matrix operator*(const matrix& x) { matrix res({{0, 0, 0}, {0, 0, 0}, {0, 0, 0}}); rep(i, 3) rep(j, 3) rep(k, 3) { // cout << i << "," << j << " <- " << a[i][k] << "*" << x.a[k][j] << endl; res.a[i][j] += a[i][k] * x.a[k][j]; } return res; } vector operator*(const vector& x) { matrix other({{x[0], 0, 0}, {x[1], 0, 0}, {1, 0, 0}}); auto res = *this * other; return vector({res.a[0][0], res.a[1][0], res.a[2][0]}); } }; int main() { cin.tie(nullptr); ios_base::sync_with_stdio(false); cout << fixed << setprecision(15); ll A, B, C; cin >> A >> B >> C; auto is_ok = [&](ll x) -> bool { ll n = x / A; if (C <= (x - n)) { return true; } if (n < (C - (x - n)) / B) { return false; } return x - n + n * B >= C; }; ll ok = 1e18; ll ng = 0; while (abs(ok - ng) > 1) { ll mid = (ok + ng) / 2; if (is_ok(mid)) { ok = mid; } else { ng = mid; } } cout << ok << endl; return 0; }