#include #include #include #include #include #define _USE_MATH_DEFINES #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include using namespace std; #define FOR(i,m,n) for(int i=(m);i<(n);++i) #define REP(i,n) FOR(i,0,n) #define ALL(v) (v).begin(),(v).end() const int INF = 0x3f3f3f3f; const long long LINF = 0x3f3f3f3f3f3f3f3fLL; const double EPS = 1e-8; const int MOD = 1000000007; // 998244353; const int dy[] = {1, 0, -1, 0}, dx[] = {0, -1, 0, 1}; /*-------------------------------------------------*/ // https://gist.github.com/ar-pa/957297fb3f88996ead11 const int base = 1000000000; const int base_digits = 9; struct bigint { vector a; int sign; /**/ int size(){ if(a.empty())return 0; int ans=(a.size()-1)*base_digits; int ca=a.back(); while(ca) ans++,ca/=10; return ans; } bigint operator ^(const bigint &v){ bigint ans=1,a=*this,b=v; while(!b.isZero()){ if(b%2) ans*=a; a*=a,b/=2; } return ans; } string to_string(){ stringstream ss; ss << *this; string s; ss >> s; return s; } int sumof(){ string s = to_string(); int ans = 0; for(auto c : s) ans += c - '0'; return ans; } /**/ bigint() : sign(1) { } bigint(long long v) { *this = v; } bigint(const string &s) { read(s); } void operator=(const bigint &v) { sign = v.sign; a = v.a; } void operator=(long long v) { sign = 1; a.clear(); if (v < 0) sign = -1, v = -v; for (; v > 0; v = v / base) a.push_back(v % base); } bigint operator+(const bigint &v) const { if (sign == v.sign) { bigint res = v; for (int i = 0, carry = 0; i < (int) max(a.size(), v.a.size()) || carry; ++i) { if (i == (int) res.a.size()) res.a.push_back(0); res.a[i] += carry + (i < (int) a.size() ? a[i] : 0); carry = res.a[i] >= base; if (carry) res.a[i] -= base; } return res; } return *this - (-v); } bigint operator-(const bigint &v) const { if (sign == v.sign) { if (abs() >= v.abs()) { bigint res = *this; for (int i = 0, carry = 0; i < (int) v.a.size() || carry; ++i) { res.a[i] -= carry + (i < (int) v.a.size() ? v.a[i] : 0); carry = res.a[i] < 0; if (carry) res.a[i] += base; } res.trim(); return res; } return -(v - *this); } return *this + (-v); } void operator*=(int v) { if (v < 0) sign = -sign, v = -v; for (int i = 0, carry = 0; i < (int) a.size() || carry; ++i) { if (i == (int) a.size()) a.push_back(0); long long cur = a[i] * (long long) v + carry; carry = (int) (cur / base); a[i] = (int) (cur % base); //asm("divl %%ecx" : "=a"(carry), "=d"(a[i]) : "A"(cur), "c"(base)); } trim(); } bigint operator*(int v) const { bigint res = *this; res *= v; return res; } void operator*=(long long v) { if (v < 0) sign = -sign, v = -v; for (int i = 0, carry = 0; i < (int) a.size() || carry; ++i) { if (i == (int) a.size()) a.push_back(0); long long cur = a[i] * (long long) v + carry; carry = (int) (cur / base); a[i] = (int) (cur % base); //asm("divl %%ecx" : "=a"(carry), "=d"(a[i]) : "A"(cur), "c"(base)); } trim(); } bigint operator*(long long v) const { bigint res = *this; res *= v; return res; } friend pair divmod(const bigint &a1, const bigint &b1) { int norm = base / (b1.a.back() + 1); bigint a = a1.abs() * norm; bigint b = b1.abs() * norm; bigint q, r; q.a.resize(a.a.size()); for (int i = a.a.size() - 1; i >= 0; i--) { r *= base; r += a.a[i]; int s1 = r.a.size() <= b.a.size() ? 0 : r.a[b.a.size()]; int s2 = r.a.size() <= b.a.size() - 1 ? 0 : r.a[b.a.size() - 1]; int d = ((long long) base * s1 + s2) / b.a.back(); r -= b * d; while (r < 0) r += b, --d; q.a[i] = d; } q.sign = a1.sign * b1.sign; r.sign = a1.sign; q.trim(); r.trim(); return make_pair(q, r / norm); } bigint operator/(const bigint &v) const { return divmod(*this, v).first; } bigint operator%(const bigint &v) const { return divmod(*this, v).second; } void operator/=(int v) { if (v < 0) sign = -sign, v = -v; for (int i = (int) a.size() - 1, rem = 0; i >= 0; --i) { long long cur = a[i] + rem * (long long) base; a[i] = (int) (cur / v); rem = (int) (cur % v); } trim(); } bigint operator/(int v) const { bigint res = *this; res /= v; return res; } int operator%(int v) const { if (v < 0) v = -v; int m = 0; for (int i = a.size() - 1; i >= 0; --i) m = (a[i] + m * (long long) base) % v; return m * sign; } void operator+=(const bigint &v) { *this = *this + v; } void operator-=(const bigint &v) { *this = *this - v; } void operator*=(const bigint &v) { *this = *this * v; } void operator/=(const bigint &v) { *this = *this / v; } bool operator<(const bigint &v) const { if (sign != v.sign) return sign < v.sign; if (a.size() != v.a.size()) return a.size() * sign < v.a.size() * v.sign; for (int i = a.size() - 1; i >= 0; i--) if (a[i] != v.a[i]) return a[i] * sign < v.a[i] * sign; return false; } bool operator>(const bigint &v) const { return v < *this; } bool operator<=(const bigint &v) const { return !(v < *this); } bool operator>=(const bigint &v) const { return !(*this < v); } bool operator==(const bigint &v) const { return !(*this < v) && !(v < *this); } bool operator!=(const bigint &v) const { return *this < v || v < *this; } void trim() { while (!a.empty() && !a.back()) a.pop_back(); if (a.empty()) sign = 1; } bool isZero() const { return a.empty() || (a.size() == 1 && !a[0]); } bigint operator-() const { bigint res = *this; res.sign = -sign; return res; } bigint abs() const { bigint res = *this; res.sign *= res.sign; return res; } long long longValue() const { long long res = 0; for (int i = a.size() - 1; i >= 0; i--) res = res * base + a[i]; return res * sign; } friend bigint gcd(const bigint &a, const bigint &b) { return b.isZero() ? a : gcd(b, a % b); } friend bigint lcm(const bigint &a, const bigint &b) { return a / gcd(a, b) * b; } void read(const string &s) { sign = 1; a.clear(); int pos = 0; while (pos < (int) s.size() && (s[pos] == '-' || s[pos] == '+')) { if (s[pos] == '-') sign = -sign; ++pos; } for (int i = s.size() - 1; i >= pos; i -= base_digits) { int x = 0; for (int j = max(pos, i - base_digits + 1); j <= i; j++) x = x * 10 + s[j] - '0'; a.push_back(x); } trim(); } friend istream& operator>>(istream &stream, bigint &v) { string s; stream >> s; v.read(s); return stream; } friend ostream& operator<<(ostream &stream, const bigint &v) { if (v.sign == -1) stream << '-'; stream << (v.a.empty() ? 0 : v.a.back()); for (int i = (int) v.a.size() - 2; i >= 0; --i) stream << setw(base_digits) << setfill('0') << v.a[i]; return stream; } static vector convert_base(const vector &a, int old_digits, int new_digits) { vector p(max(old_digits, new_digits) + 1); p[0] = 1; for (int i = 1; i < (int) p.size(); i++) p[i] = p[i - 1] * 10; vector res; long long cur = 0; int cur_digits = 0; for (int i = 0; i < (int) a.size(); i++) { cur += a[i] * p[cur_digits]; cur_digits += old_digits; while (cur_digits >= new_digits) { res.push_back(int(cur % p[new_digits])); cur /= p[new_digits]; cur_digits -= new_digits; } } res.push_back((int) cur); while (!res.empty() && !res.back()) res.pop_back(); return res; } typedef vector vll; static vll karatsubaMultiply(const vll &a, const vll &b) { int n = a.size(); vll res(n + n); if (n <= 32) { for (int i = 0; i < n; i++) for (int j = 0; j < n; j++) res[i + j] += a[i] * b[j]; return res; } int k = n >> 1; vll a1(a.begin(), a.begin() + k); vll a2(a.begin() + k, a.end()); vll b1(b.begin(), b.begin() + k); vll b2(b.begin() + k, b.end()); vll a1b1 = karatsubaMultiply(a1, b1); vll a2b2 = karatsubaMultiply(a2, b2); for (int i = 0; i < k; i++) a2[i] += a1[i]; for (int i = 0; i < k; i++) b2[i] += b1[i]; vll r = karatsubaMultiply(a2, b2); for (int i = 0; i < (int) a1b1.size(); i++) r[i] -= a1b1[i]; for (int i = 0; i < (int) a2b2.size(); i++) r[i] -= a2b2[i]; for (int i = 0; i < (int) r.size(); i++) res[i + k] += r[i]; for (int i = 0; i < (int) a1b1.size(); i++) res[i] += a1b1[i]; for (int i = 0; i < (int) a2b2.size(); i++) res[i + n] += a2b2[i]; return res; } bigint operator*(const bigint &v) const { vector a6 = convert_base(this->a, base_digits, 6); vector b6 = convert_base(v.a, base_digits, 6); vll a(a6.begin(), a6.end()); vll b(b6.begin(), b6.end()); while (a.size() < b.size()) a.push_back(0); while (b.size() < a.size()) b.push_back(0); while (a.size() & (a.size() - 1)) a.push_back(0), b.push_back(0); vll c = karatsubaMultiply(a, b); bigint res; res.sign = sign * v.sign; for (int i = 0, carry = 0; i < (int) c.size(); i++) { long long cur = c[i] + carry; res.a.push_back((int) (cur % 1000000)); carry = (int) (cur / 1000000); } res.a = convert_base(res.a, 6, base_digits); res.trim(); return res; } }; long long __lcm(long long a, long long b) { return a / __gcd(a, b) * b; } int main() { cin.tie(nullptr); ios::sync_with_stdio(false); // freopen("input.txt", "r", stdin); long long t, a, b; cin >> t >> a >> b; long long ans = (t - 1) / a + 1 + (t - 1) / b + 1; bigint l(a / __gcd(a, b)); l *= b; if (l <= bigint(1000000000000000000)) ans -= (t - 1) / __lcm(a, b); --ans; cout << ans << '\n'; return 0; }