#include using namespace std; #define rep(i, n) for (int i = 0; i < (n); i++) #define per(i, n) for (int i = (n)-1; i >= 0; i--) #define rep2(i, l, r) for (int i = (l); i < (r); i++) #define per2(i, l, r) for (int i = (r)-1; i >= (l); i--) #define each(e, v) for (auto &e : v) #define MM << " " << #define pb push_back #define eb emplace_back #define all(x) begin(x), end(x) #define rall(x) rbegin(x), rend(x) #define sz(x) (int)x.size() using ll = long long; using pii = pair; using pil = pair; using pli = pair; using pll = pair; template using minheap = priority_queue, greater>; template using maxheap = priority_queue; template bool chmax(T &x, const T &y) { return (x < y) ? (x = y, true) : false; } template bool chmin(T &x, const T &y) { return (x > y) ? (x = y, true) : false; } template int flg(T x, int i) { return (x >> i) & 1; } template void print(const vector &v, T x = 0) { int n = v.size(); for (int i = 0; i < n; i++) cout << v[i] + x << (i == n - 1 ? '\n' : ' '); if (v.empty()) cout << '\n'; } template void printn(const vector &v, T x = 0) { int n = v.size(); for (int i = 0; i < n; i++) cout << v[i] + x << '\n'; } template int lb(const vector &v, T x) { return lower_bound(begin(v), end(v), x) - begin(v); } template int ub(const vector &v, T x) { return upper_bound(begin(v), end(v), x) - begin(v); } template void rearrange(vector &v) { sort(begin(v), end(v)); v.erase(unique(begin(v), end(v)), end(v)); } template vector id_sort(const vector &v, bool greater = false) { int n = v.size(); vector ret(n); iota(begin(ret), end(ret), 0); sort(begin(ret), end(ret), [&](int i, int j) { return greater ? v[i] > v[j] : v[i] < v[j]; }); return ret; } template pair operator+(const pair &p, const pair &q) { return make_pair(p.first + q.first, p.second + q.second); } template pair operator-(const pair &p, const pair &q) { return make_pair(p.first - q.first, p.second - q.second); } template istream &operator>>(istream &is, pair &p) { S a; T b; is >> a >> b; p = make_pair(a, b); return is; } template ostream &operator<<(ostream &os, const pair &p) { return os << p.first << ' ' << p.second; } struct io_setup { io_setup() { ios_base::sync_with_stdio(false); cin.tie(NULL); cout << fixed << setprecision(15); } } io_setup; const int inf = (1 << 30) - 1; const ll INF = (1LL << 60) - 1; // const int MOD = 1000000007; const int MOD = 998244353; struct Runtime_Mod_Int { int x; Runtime_Mod_Int() : x(0) {} Runtime_Mod_Int(long long y) { x = y % get_mod(); if (x < 0) x += get_mod(); } static inline int &get_mod() { static int mod = 0; return mod; } static void set_mod(int md) { get_mod() = md; } Runtime_Mod_Int &operator+=(const Runtime_Mod_Int &p) { if ((x += p.x) >= get_mod()) x -= get_mod(); return *this; } Runtime_Mod_Int &operator-=(const Runtime_Mod_Int &p) { if ((x += get_mod() - p.x) >= get_mod()) x -= get_mod(); return *this; } Runtime_Mod_Int &operator*=(const Runtime_Mod_Int &p) { x = (int)(1LL * x * p.x % get_mod()); return *this; } Runtime_Mod_Int &operator/=(const Runtime_Mod_Int &p) { *this *= p.inverse(); return *this; } Runtime_Mod_Int &operator++() { return *this += Runtime_Mod_Int(1); } Runtime_Mod_Int operator++(int) { Runtime_Mod_Int tmp = *this; ++*this; return tmp; } Runtime_Mod_Int &operator--() { return *this -= Runtime_Mod_Int(1); } Runtime_Mod_Int operator--(int) { Runtime_Mod_Int tmp = *this; --*this; return tmp; } Runtime_Mod_Int operator-() const { return Runtime_Mod_Int(-x); } Runtime_Mod_Int operator+(const Runtime_Mod_Int &p) const { return Runtime_Mod_Int(*this) += p; } Runtime_Mod_Int operator-(const Runtime_Mod_Int &p) const { return Runtime_Mod_Int(*this) -= p; } Runtime_Mod_Int operator*(const Runtime_Mod_Int &p) const { return Runtime_Mod_Int(*this) *= p; } Runtime_Mod_Int operator/(const Runtime_Mod_Int &p) const { return Runtime_Mod_Int(*this) /= p; } bool operator==(const Runtime_Mod_Int &p) const { return x == p.x; } bool operator!=(const Runtime_Mod_Int &p) const { return x != p.x; } Runtime_Mod_Int inverse() const { assert(*this != Runtime_Mod_Int(0)); return pow(get_mod() - 2); } Runtime_Mod_Int pow(long long k) const { Runtime_Mod_Int now = *this, ret = 1; for (; k > 0; k >>= 1, now *= now) { if (k & 1) ret *= now; } return ret; } friend ostream &operator<<(ostream &os, const Runtime_Mod_Int &p) { return os << p.x; } friend istream &operator>>(istream &is, Runtime_Mod_Int &p) { long long a; is >> a; p = Runtime_Mod_Int(a); return is; } }; using mint = Runtime_Mod_Int; template struct Combination { static vector _fac, _ifac; Combination() {} static void init(int n) { _fac.resize(n + 1), _ifac.resize(n + 1); _fac[0] = 1; for (int i = 1; i <= n; i++) _fac[i] = _fac[i - 1] * i; _ifac[n] = _fac[n].inverse(); for (int i = n; i >= 1; i--) _ifac[i - 1] = _ifac[i] * i; } static T fac(int k) { return _fac[k]; } static T ifac(int k) { return _ifac[k]; } static T inv(int k) { return fac(k - 1) * ifac(k); } static T P(int n, int k) { if (k < 0 || n < k) return 0; return fac(n) * ifac(n - k); } static T C(int n, int k) { if (k < 0 || n < k) return 0; return fac(n) * ifac(n - k) * ifac(k); } // k 個の区別できない玉を n 個の区別できる箱に入れる場合の数 static T H(int n, int k) { if (n < 0 || k < 0) return 0; return k == 0 ? 1 : C(n + k - 1, k); } // n 個の区別できる玉を、k 個の区別しない箱に、各箱に 1 個以上玉が入るように入れる場合の数 static T second_stirling_number(int n, int k) { T ret = 0; for (int i = 0; i <= k; i++) { T tmp = C(k, i) * T(i).pow(n); ret += ((k - i) & 1) ? -tmp : tmp; } return ret * ifac(k); } // n 個の区別できる玉を、k 個の区別しない箱に入れる場合の数 static T bell_number(int n, int k) { if (n == 0) return 1; k = min(k, n); vector pref(k + 1); pref[0] = 1; for (int i = 1; i <= k; i++) { if (i & 1) { pref[i] = pref[i - 1] - ifac(i); } else { pref[i] = pref[i - 1] + ifac(i); } } T ret = 0; for (int i = 1; i <= k; i++) ret += T(i).pow(n) * ifac(i) * pref[k - i]; return ret; } }; template vector Combination::_fac = vector(); template vector Combination::_ifac = vector(); template vector divisors(const T &n) { vector ret; for (T i = 1; i * i <= n; i++) { if (n % i == 0) { ret.push_back(i); if (i * i != n) ret.push_back(n / i); } } sort(begin(ret), end(ret)); return ret; } template vector> prime_factor(T n) { vector> ret; for (T i = 2; i * i <= n; i++) { int cnt = 0; while (n % i == 0) cnt++, n /= i; if (cnt > 0) ret.emplace_back(i, cnt); } if (n > 1) ret.emplace_back(n, 1); return ret; } template bool is_prime(const T &n) { if (n == 1) return false; for (T i = 2; i * i <= n; i++) { if (n % i == 0) return false; } return true; } // 1,2,...,n のうち k と互いに素である自然数の個数 template T coprime(T n, T k) { vector> ps = prime_factor(k); int m = ps.size(); T ret = 0; for (int i = 0; i < (1 << m); i++) { T prd = 1; for (int j = 0; j < m; j++) { if ((i >> j) & 1) prd *= ps[j].first; } ret += (__builtin_parity(i) ? -1 : 1) * (n / prd); } return ret; } vector Eratosthenes(const int &n) { vector ret(n + 1, true); if (n >= 0) ret[0] = false; if (n >= 1) ret[1] = false; for (int i = 2; i * i <= n; i++) { if (!ret[i]) continue; for (int j = i + i; j <= n; j += i) ret[j] = false; } return ret; } vector Eratosthenes2(const int &n) { vector ret(n + 1); iota(begin(ret), end(ret), 0); if (n >= 0) ret[0] = -1; if (n >= 1) ret[1] = -1; for (int i = 2; i * i <= n; i++) { if (ret[i] < i) continue; for (int j = i + i; j <= n; j += i) ret[j] = min(ret[j], i); } return ret; } struct Random_Number_Generator { mt19937_64 mt; Random_Number_Generator() : mt(chrono::steady_clock::now().time_since_epoch().count()) {} // [l,r) での一様乱数 int64_t operator()(int64_t l, int64_t r) { uniform_int_distribution dist(l, r - 1); return dist(mt); } // [0,r) での一様乱数 int64_t operator()(int64_t r) { return (*this)(0, r); } } rng; long long modpow(long long x, long long n, const int &m) { x %= m; long long ret = 1; for (; n > 0; n >>= 1, x *= x, x %= m) { if (n & 1) ret *= x, ret %= m; } return ret; } template T modinv(T a, const T &m) { T b = m, u = 1, v = 0; while (b > 0) { T t = a / b; swap(a -= t * b, b); swap(u -= t * v, v); } return u >= 0 ? u % m : (m - (-u) % m) % m; } // オイラーの φ 関数 (x と m が互いに素ならば、x^φ(m) ≡ 1 (mod m)) template T Euler_totient(T m) { T ret = m; for (T i = 2; i * i <= m; i++) { if (m % i == 0) ret /= i, ret *= i - 1; while (m % i == 0) m /= i; } if (m > 1) ret /= m, ret *= m - 1; return ret; } // x^k ≡ y (mod m) となる最小の非負整数 k (存在しなければ -1) int modlog(int x, int y, int m, int max_ans = -1) { if (max_ans == -1) max_ans = m; long long g = 1; for (int i = m; i > 0; i >>= 1) g *= x, g %= m; g = gcd(g, m); int c = 0; long long t = 1; for (; t % g != 0; c++) { if (t == y) return c; t *= x, t %= m; } if (y % g != 0) return -1; t /= g, y /= g, m /= g; int n = 0; long long gs = 1; for (; n * n < max_ans; n++) gs *= x, gs %= m; unordered_map mp; long long e = y; for (int i = 0; i < n; mp[e] = ++i) e *= x, e %= m; e = t; for (int i = 0; i < n; i++) { e *= gs, e %= m; if (mp.count(e)) return c + n * (i + 1) - mp[e]; } return -1; } // x^k ≡ 1 (mod m) となる最小の正整数 k (x と m は互いに素) template T order(T x, const T &m) { T n = Euler_totient(m); vector ds; for (T i = 1; i * i <= n; i++) { if (n % i == 0) ds.push_back(i), ds.push_back(n / i); } sort(begin(ds), end(ds)); for (auto &e : ds) { if (modpow(x, e, m) == 1) return e; } return -1; } // 素数 p の原始根 template T primitive_root(const T &p) { vector ds; for (T i = 1; i * i <= p - 1; i++) { if ((p - 1) % i == 0) ds.push_back(i), ds.push_back((p - 1) / i); } sort(begin(ds), end(ds)); while (true) { T r = rng(1, p); for (auto &e : ds) { if (e == p - 1) return r; if (modpow(r, e, p) == 1) break; } } } template T _gcd(const T &a, const T &b) { if (b == 0) return a; return _gcd(b, a % b); } template T _lcm(const T &a, const T &b) { return a * (b / _gcd(a, b)); } // |x| と |y| は結果として max(a,b) 以下になる。 template T extgcd(const T &a, const T &b, T &x, T &y) { if (b == 0) { x = 1, y = 0; return a; } T g = extgcd(b, a % b, y, x); y -= (a / b) * x; return g; } int mod(const long long &a, const int &m) { int ret = a % m; return ret + (ret < 0 ? m : 0); } // a と m は互いに素 int modinv(const int &a, const int &m) { int x, y; extgcd(a, m, x, y); return mod(x, m); } // Σ[0<=i T floor_sum(const T &n, const T &m, T a, T b) { T ret = (a / m) * (n * (n - 1) / 2) + (b / m) * n; a %= m, b %= m; T y = (a * n + b) / m; if (y == 0) return ret; ret += floor_sum(y, a, m, a * n - (m * y - b)); return ret; } // min{ai+b mod m | 0<=i T linear_mod_min(T n, const T &m, T a, T b, bool is_min = true, T p = 1, T q = 1) { if (a == 0) return b; if (is_min) { if (b >= a) { T t = (m - b + a - 1) / a; T c = (t - 1) * p + q; if (n <= c) return b; n -= c; b += a * t - m; } b = a - 1 - b; } else { if (b < m - a) { T t = (m - b - 1) / a; T c = t * p; if (n <= c) return a * ((n - 1) / p) + b; n -= c; b += a * t; } b = m - 1 - b; } T d = m / a; T c = linear_mod_min(n, a, m % a, b, !is_min, (d - 1) * p + q, d * p + q); return is_min ? a - 1 - c : m - 1 - c; } template pair Chinese_remainder_theorem(const T &a1, const T &m1, const T &a2, const T &m2) { T x, y, g = extgcd(m1, m2, x, y); if ((a2 - a1) % g != 0) return make_pair(0, -1); T m = m1 * (m2 / g); T tmp = mod(x * ((a2 - a1) / g), m2 / g); T a = (m1 * tmp + a1) % m; return make_pair(a, m); } // m の各要素がそれぞれ互いに素とは限らない場合の前処理 bool prepare_Garner(vector &a, vector &m) { int n = a.size(); for (int i = 0; i < n; i++) { for (int j = 0; j < i; j++) { int g = gcd(m[i], m[j]); if ((a[i] - a[j]) % g != 0) return false; m[i] /= g, m[j] /= g; int gi = gcd(m[i], g), gj = g / gi; do { g = gcd(gi, gj); gi *= g, gj /= g; } while (g > 1); m[i] *= gi, m[j] *= gj; } } return true; } // m の各要素はそれぞれ互いに素 int Garner(vector a, vector m, const int &M) { m.push_back(M); vector coeffs(m.size(), 1); vector constants(m.size(), 0); for (int k = 0; k < (int)a.size(); k++) { long long x = a[k] - constants[k], y = modinv(coeffs[k], m[k]); long long t = mod(x * y, m[k]); for (int i = k + 1; i < (int)m.size(); i++) { constants[i] += t * coeffs[i], constants[i] %= m[i]; coeffs[i] *= m[k], coeffs[i] %= m[i]; } } return constants.back(); } int main() { ll L, R, M; cin >> L >> R >> M; if (M == 1) { cout << "0\n"; return 0; } auto ps = prime_factor(M); auto solve = [&](ll l, ll r, ll p, ll c) { ll q = 1; rep(i, c) q *= p; vector fac(q, 1), ifac(q, 1); rep2(i, 1, q) { ll x = i; while (x % p == 0) x /= p; if (x != i) x = 1; fac[i] = fac[i - 1] * x % q; ifac[i] = modinv(fac[i], q); } // print(fac), print(ifac); auto calc1 = [&](ll n) { ll cnt = 0; while (n > 0) { cnt += n / p; n /= p; } return cnt; }; auto calc2 = [&](ll n) { ll ret = 1; while (n > 0) { ll t = n / q, m = n % q; ret *= modpow(fac[q - 1], t, q), ret %= q; ret *= fac[m], ret %= q; n /= p; } return ret; }; auto calc3 = [&](ll n) { ll ret = 1; while (n > 0) { ll t = n / q, m = n % q; ret *= modpow(ifac[q - 1], t, q), ret %= q; ret *= ifac[m], ret %= q; n /= p; } return ret; }; ll ret = 0; ll c1 = calc1(2 * l), m1 = calc2(2 * l); ll c2 = calc1(l), m2 = calc3(l); for (ll n = l; n <= r; n++) { ll t = min(c1 - c2 * 2, c); ll tmp = (m1 * m2 * m2) % q; rep(i, t) tmp *= p, tmp %= q; ret += tmp, ret %= q; // cout << c1 MM m1 MM c2 MM m2 MM tmp << '\n'; for (ll i = 2 * n + 1; i <= 2 * n + 2; i++) { ll x = i; while (x % p == 0) x /= p, c1++; x %= q; m1 *= x, m1 %= q; } for (ll i = n + 1; i <= n + 1; i++) { ll x = i; while (x % p == 0) x /= p, c2++; x %= q; m2 *= modinv(x, q), m2 %= q; } } return ret; }; vector as, ms; for (auto [p, c] : ps) { ll q = 1; rep(i, c) q *= p; as.eb(solve(L, R, p, c)); ms.eb(q); } ll ans = Garner(as, ms, M); ans += M - ((R - L + 1) * 2) % M; ans %= M; cout << ans << '\n'; }