#line 1 "test.cpp" //#pragma GCC target("avx2") //#pragma GCC optimize("O3") //#pragma GCC optimize("unroll-loops") #include using namespace std; #ifdef LOCAL #include #define debug(...) debug_print::multi_print(#__VA_ARGS__, __VA_ARGS__) #else #define debug(...) (static_cast(0)) #endif using ll = long long; using ld = long double; using pll = pair; using pii = pair; using vi = vector; using vvi = vector; using vvvi = vector; using vl = vector; using vvl = vector; using vvvl = vector; using vpii = vector; using vpll = vector; using vs = vector; template using pq = priority_queue,greater>; #define overload4(_1, _2, _3, _4, name, ...) name #define overload3(a,b,c,name,...) name #define rep1(n) for (ll UNUSED_NUMBER = 0; UNUSED_NUMBER < (n); ++UNUSED_NUMBER) #define rep2(i, n) for (ll i = 0; i < (n); ++i) #define rep3(i, a, b) for (ll i = (a); i < (b); ++i) #define rep4(i, a, b, c) for (ll i = (a); i < (b); i += (c)) #define rep(...) overload4(__VA_ARGS__, rep4, rep3, rep2, rep1)(__VA_ARGS__) #define rrep1(n) for(ll i = (n) - 1;i >= 0;i--) #define rrep2(i,n) for(ll i = (n) - 1;i >= 0;i--) #define rrep3(i,a,b) for(ll i = (b) - 1;i >= (a);i--) #define rrep4(i,a,b,c) for(ll i = (a) + ((b)-(a)-1) / (c) * (c);i >= (a);i -= c) #define rrep(...) overload4(__VA_ARGS__, rrep4, rrep3, rrep2, rrep1)(__VA_ARGS__) #define all1(i) begin(i),end(i) #define all2(i,a) begin(i),begin(i)+a #define all3(i,a,b) begin(i)+a,begin(i)+b #define all(...) overload3(__VA_ARGS__, all3, all2, all1)(__VA_ARGS__) #define sum(...) accumulate(all(__VA_ARGS__),0LL) template bool chmin(T &a, const T &b){ if(a > b){ a = b; return 1; } else return 0; } template bool chmax(T &a, const T &b){ if(a < b){ a = b; return 1; } else return 0; } template auto min(const T& a){ return *min_element(all(a)); } template auto max(const T& a){ return *max_element(all(a)); } template void in(Ts&... t); #define INT(...) int __VA_ARGS__; in(__VA_ARGS__) #define LL(...) ll __VA_ARGS__; in(__VA_ARGS__) #define STR(...) string __VA_ARGS__; in(__VA_ARGS__) #define CHR(...) char __VA_ARGS__; in(__VA_ARGS__) #define DBL(...) double __VA_ARGS__; in(__VA_ARGS__) #define LD(...) ld __VA_ARGS__; in(__VA_ARGS__) #define VEC(type, name, size) vector name(size); in(name) #define VV(type, name, h, w) vector> name(h, vector(w)); in(name) ll intpow(ll a, ll b){ ll ans = 1; while(b){if(b & 1) ans *= a; a *= a; b /= 2;} return ans;} ll modpow(ll a, ll b, ll p){ ll ans = 1; a %= p;while(b){ if(b & 1) (ans *= a) %= p; (a *= a) %= p; b /= 2; } return ans; } ll GCD(ll a,ll b) { if(a == 0 || b == 0) return a + b; if(a % b == 0) return b; else return GCD(b,a%b);} ll LCM(ll a,ll b) { if(a == 0) return b; if(b == 0) return a;return a / GCD(a,b) * b;} namespace IO{ #define VOID(a) decltype(void(a)) struct setting{ setting(){cin.tie(nullptr); ios::sync_with_stdio(false);fixed(cout); cout.precision(12);}} setting; template struct P : P{}; template<> struct P<0>{}; template void i(T& t){ i(t, P<3>{}); } void i(vector::reference t, P<3>){ int a; i(a); t = a; } template auto i(T& t, P<2>) -> VOID(cin >> t){ cin >> t; } template auto i(T& t, P<1>) -> VOID(begin(t)){ for(auto&& x : t) i(x); } template void ituple(T& t, index_sequence){ in(get(t)...);} template auto i(T& t, P<0>) -> VOID(tuple_size{}){ ituple(t, make_index_sequence::value>{});} #undef VOID } #define unpack(a) (void)initializer_list{(a, 0)...} template void in(Ts&... t){ unpack(IO :: i(t)); } #undef unpack constexpr int mod = 1000000007; //constexpr int mod = 998244353; static const double PI = 3.1415926535897932; template struct REC { F f; REC(F &&f_) : f(forward(f_)) {} template auto operator()(Args &&...args) const { return f(*this, forward(args)...); }}; #line 2 "modulo/arbitrary-mod-binomial.hpp" #line 89 "test.cpp" #line 1 "atcoder/math.hpp" #line 97 "test.cpp" #line 8 "atcoder/math.hpp" #line 1 "atcoder/internal_math.hpp" #line 104 "test.cpp" #ifdef _MSC_VER #include #endif namespace atcoder { namespace internal { // @param m `1 <= m` // @return x mod m constexpr long long safe_mod(long long x, long long m) { x %= m; if (x < 0) x += m; return x; } // Fast modular multiplication by barrett reduction // Reference: https://en.wikipedia.org/wiki/Barrett_reduction // NOTE: reconsider after Ice Lake struct barrett { unsigned int _m; unsigned long long im; // @param m `1 <= m < 2^31` barrett(unsigned int m) : _m(m), im((unsigned long long)(-1) / m + 1) {} // @return m unsigned int umod() const { return _m; } // @param a `0 <= a < m` // @param b `0 <= b < m` // @return `a * b % m` unsigned int mul(unsigned int a, unsigned int b) const { // [1] m = 1 // a = b = im = 0, so okay // [2] m >= 2 // im = ceil(2^64 / m) // -> im * m = 2^64 + r (0 <= r < m) // let z = a*b = c*m + d (0 <= c, d < m) // a*b * im = (c*m + d) * im = c*(im*m) + d*im = c*2^64 + c*r + d*im // c*r + d*im < m * m + m * im < m * m + 2^64 + m <= 2^64 + m * (m + 1) < 2^64 * 2 // ((ab * im) >> 64) == c or c + 1 unsigned long long z = a; z *= b; #ifdef _MSC_VER unsigned long long x; _umul128(z, im, &x); #else unsigned long long x = (unsigned long long)(((unsigned __int128)(z)*im) >> 64); #endif unsigned int v = (unsigned int)(z - x * _m); if (_m <= v) v += _m; return v; } }; // @param n `0 <= n` // @param m `1 <= m` // @return `(x ** n) % m` constexpr long long pow_mod_constexpr(long long x, long long n, int m) { if (m == 1) return 0; unsigned int _m = (unsigned int)(m); unsigned long long r = 1; unsigned long long y = safe_mod(x, m); while (n) { if (n & 1) r = (r * y) % _m; y = (y * y) % _m; n >>= 1; } return r; } // Reference: // M. Forisek and J. Jancina, // Fast Primality Testing for Integers That Fit into a Machine Word // @param n `0 <= n` constexpr bool is_prime_constexpr(int n) { if (n <= 1) return false; if (n == 2 || n == 7 || n == 61) return true; if (n % 2 == 0) return false; long long d = n - 1; while (d % 2 == 0) d /= 2; constexpr long long bases[3] = {2, 7, 61}; for (long long a : bases) { long long t = d; long long y = pow_mod_constexpr(a, t, n); while (t != n - 1 && y != 1 && y != n - 1) { y = y * y % n; t <<= 1; } if (y != n - 1 && t % 2 == 0) { return false; } } return true; } template constexpr bool is_prime = is_prime_constexpr(n); // @param b `1 <= b` // @return pair(g, x) s.t. g = gcd(a, b), xa = g (mod b), 0 <= x < b/g constexpr std::pair inv_gcd(long long a, long long b) { a = safe_mod(a, b); if (a == 0) return {b, 0}; // Contracts: // [1] s - m0 * a = 0 (mod b) // [2] t - m1 * a = 0 (mod b) // [3] s * |m1| + t * |m0| <= b long long s = b, t = a; long long m0 = 0, m1 = 1; while (t) { long long u = s / t; s -= t * u; m0 -= m1 * u; // |m1 * u| <= |m1| * s <= b // [3]: // (s - t * u) * |m1| + t * |m0 - m1 * u| // <= s * |m1| - t * u * |m1| + t * (|m0| + |m1| * u) // = s * |m1| + t * |m0| <= b auto tmp = s; s = t; t = tmp; tmp = m0; m0 = m1; m1 = tmp; } // by [3]: |m0| <= b/g // by g != b: |m0| < b/g if (m0 < 0) m0 += b / s; return {s, m0}; } // Compile time primitive root // @param m must be prime // @return primitive root (and minimum in now) constexpr int primitive_root_constexpr(int m) { if (m == 2) return 1; if (m == 167772161) return 3; if (m == 469762049) return 3; if (m == 754974721) return 11; if (m == 998244353) return 3; int divs[20] = {}; divs[0] = 2; int cnt = 1; int x = (m - 1) / 2; while (x % 2 == 0) x /= 2; for (int i = 3; (long long)(i)*i <= x; i += 2) { if (x % i == 0) { divs[cnt++] = i; while (x % i == 0) { x /= i; } } } if (x > 1) { divs[cnt++] = x; } for (int g = 2;; g++) { bool ok = true; for (int i = 0; i < cnt; i++) { if (pow_mod_constexpr(g, (m - 1) / divs[i], m) == 1) { ok = false; break; } } if (ok) return g; } } template constexpr int primitive_root = primitive_root_constexpr(m); } // namespace internal } // namespace atcoder #line 10 "atcoder/math.hpp" namespace atcoder { long long pow_mod(long long x, long long n, int m) { assert(0 <= n && 1 <= m); if (m == 1) return 0; internal::barrett bt((unsigned int)(m)); unsigned int r = 1, y = (unsigned int)(internal::safe_mod(x, m)); while (n) { if (n & 1) r = bt.mul(r, y); y = bt.mul(y, y); n >>= 1; } return r; } long long inv_mod(long long x, long long m) { assert(1 <= m); auto z = internal::inv_gcd(x, m); assert(z.first == 1); return z.second; } // (rem, mod) std::pair crt(const std::vector& r, const std::vector& m) { assert(r.size() == m.size()); int n = int(r.size()); // Contracts: 0 <= r0 < m0 long long r0 = 0, m0 = 1; for (int i = 0; i < n; i++) { assert(1 <= m[i]); long long r1 = internal::safe_mod(r[i], m[i]), m1 = m[i]; if (m0 < m1) { std::swap(r0, r1); std::swap(m0, m1); } if (m0 % m1 == 0) { if (r0 % m1 != r1) return {0, 0}; continue; } // assume: m0 > m1, lcm(m0, m1) >= 2 * max(m0, m1) // (r0, m0), (r1, m1) -> (r2, m2 = lcm(m0, m1)); // r2 % m0 = r0 // r2 % m1 = r1 // -> (r0 + x*m0) % m1 = r1 // -> x*u0*g % (u1*g) = (r1 - r0) (u0*g = m0, u1*g = m1) // -> x = (r1 - r0) / g * inv(u0) (mod u1) // im = inv(u0) (mod u1) (0 <= im < u1) long long g, im; std::tie(g, im) = internal::inv_gcd(m0, m1); long long u1 = (m1 / g); // |r1 - r0| < (m0 + m1) <= lcm(m0, m1) if ((r1 - r0) % g) return {0, 0}; // u1 * u1 <= m1 * m1 / g / g <= m0 * m1 / g = lcm(m0, m1) long long x = (r1 - r0) / g % u1 * im % u1; // |r0| + |m0 * x| // < m0 + m0 * (u1 - 1) // = m0 + m0 * m1 / g - m0 // = lcm(m0, m1) r0 += x * m0; m0 *= u1; // -> lcm(m0, m1) if (r0 < 0) r0 += m0; } return {r0, m0}; } long long floor_sum(long long n, long long m, long long a, long long b) { long long ans = 0; if (a >= m) { ans += (n - 1) * n * (a / m) / 2; a %= m; } if (b >= m) { ans += n * (b / m); b %= m; } long long y_max = (a * n + b) / m, x_max = (y_max * m - b); if (y_max == 0) return ans; ans += (n - (x_max + a - 1) / a) * y_max; ans += floor_sum(y_max, a, m, (a - x_max % a) % a); return ans; } } // namespace atcoder #line 2 "modint/barrett-reduction.hpp" #line 4 "modint/barrett-reduction.hpp" using namespace std; struct Barrett { using u32 = unsigned int; using i64 = long long; using u64 = unsigned long long; u32 m; u64 im; Barrett() : m(), im() {} Barrett(int n) : m(n), im(u64(-1) / m + 1) {} constexpr inline i64 quo(u64 n) { u64 x = u64((__uint128_t(n) * im) >> 64); u32 r = n - x * m; return m <= r ? x - 1 : x; } constexpr inline i64 rem(u64 n) { u64 x = u64((__uint128_t(n) * im) >> 64); u32 r = n - x * m; return m <= r ? r + m : r; } constexpr inline pair quorem(u64 n) { u64 x = u64((__uint128_t(n) * im) >> 64); u32 r = n - x * m; if (m <= r) return {x - 1, r + m}; return {x, r}; } constexpr inline i64 pow(u64 n, i64 p) { u32 a = rem(n), r = m == 1 ? 0 : 1; while (p) { if (p & 1) r = rem(u64(r) * a); a = rem(u64(a) * a); p >>= 1; } return r; } }; #line 7 "modulo/arbitrary-mod-binomial.hpp" using namespace std; #define PRIME_POWER_BINOMIAL_M_MAX ((1LL << 30) - 1) #define PRIME_POWER_BINOMIAL_N_MAX 20000000 struct prime_power_binomial { int p, q, M; vector fac, ifac, inv; int delta; Barrett bm, bp; prime_power_binomial(int _p, int _q) : p(_p), q(_q) { assert(1 < p && p <= PRIME_POWER_BINOMIAL_M_MAX); assert(_q > 0); long long m = 1; while (_q--) { m *= p; assert(m <= PRIME_POWER_BINOMIAL_M_MAX); } M = m; bm = Barrett(M), bp = Barrett(p); enumerate(); delta = (p == 2 && q >= 3) ? 1 : M - 1; } void enumerate() { int MX = min(M, PRIME_POWER_BINOMIAL_N_MAX + 10); fac.resize(MX); ifac.resize(MX); inv.resize(MX); fac[0] = ifac[0] = inv[0] = 1; fac[1] = ifac[1] = inv[1] = 1; for (int i = 2; i < MX; i++) { if (i % p == 0) { fac[i] = fac[i - 1]; fac[i + 1] = bm.rem(1LL * fac[i - 1] * (i + 1)); i++; } else { fac[i] = bm.rem(1LL * fac[i - 1] * i); } } ifac[MX - 1] = bm.pow(fac[MX - 1], M / p * (p - 1) - 1); for (int i = MX - 2; i > 1; --i) { if (i % p == 0) { ifac[i] = bm.rem(1LL * ifac[i + 1] * (i + 1)); ifac[i - 1] = ifac[i]; i--; } else { ifac[i] = bm.rem(1LL * ifac[i + 1] * (i + 1)); } } } long long Lucas(long long n, long long m) { int res = 1; while (n) { int n0, m0; tie(n, n0) = bp.quorem(n); tie(m, m0) = bp.quorem(m); if (n0 < m0) return 0; res = bm.rem(1LL * res * fac[n0]); int buf = bm.rem(1LL * ifac[n0 - m0] * ifac[m0]); res = bm.rem(1LL * res * buf); } return res; } long long C(long long n, long long m) { if (n < m || n < 0 || m < 0) return 0; if (q == 1) return Lucas(n, m); long long r = n - m; int e0 = 0, eq = 0, i = 0; int res = 1; while (n) { res = bm.rem(1LL * res * fac[bm.rem(n)]); res = bm.rem(1LL * res * ifac[bm.rem(m)]); res = bm.rem(1LL * res * ifac[bm.rem(r)]); n = bp.quo(n); m = bp.quo(m); r = bp.quo(r); int eps = n - m - r; e0 += eps; if (e0 >= q) return 0; if (++i >= q) eq += eps; } if (eq & 1) res = bm.rem(1LL * res * delta); res = bm.rem(1LL * res * bm.pow(p, e0)); return res; } }; // constraints: // (M <= 1e7 and max(N) <= 1e18) or (M < 2^30 and max(N) <= 2e7) struct arbitrary_mod_binomial { int mod; vector M; vector cs; arbitrary_mod_binomial(long long md) : mod(md) { assert(1 <= md); assert(md <= PRIME_POWER_BINOMIAL_M_MAX); for (int i = 2; i * i <= md; i++) { if (md % i == 0) { int j = 0, k = 1; while (md % i == 0) md /= i, j++, k *= i; M.push_back(k); cs.emplace_back(i, j); assert(M.back() == cs.back().M); } } if (md != 1) { M.push_back(md); cs.emplace_back(md, 1); } assert(M.size() == cs.size()); } long long C(long long n, long long m) { if (mod == 1) return 0; vector rem, d; for (int i = 0; i < (int)cs.size(); i++) { rem.push_back(cs[i].C(n, m)); d.push_back(M[i]); } return atcoder::crt(rem, d).first; } }; #undef PRIME_POWER_BINOMIAL_M_MAX #undef PRIME_POWER_BINOMIAL_N_MAX /** * @brief 任意mod二項係数 * @docs docs/modulo/arbitrary-mod-binomial.md */ #line 2 "library/modint/ArbitaryModint.hpp" //#include "library/modint/barrett-reduction.hpp" struct ArbitraryModint { int x; ArbitraryModint():x(0) {} ArbitraryModint(int64_t y) { int z = y % get_mod(); if(z < 0) z += get_mod(); x = z; } ArbitraryModint &operator+=(const ArbitraryModint &p) { if((x += p.x) >= get_mod()) x -= get_mod(); return *this; } ArbitraryModint &operator-=(const ArbitraryModint &p) { if((x += get_mod() - p.x) >= get_mod()) x -= get_mod(); return *this; } ArbitraryModint &operator*=(const ArbitraryModint &p) { x = rem((unsigned long long)x * p.x); return *this; } ArbitraryModint &operator/=(const ArbitraryModint &p) { *this *= p.inverse(); return *this; } ArbitraryModint operator-() const {return ArbitraryModint(-x);}; ArbitraryModint operator+(const ArbitraryModint &p) const{ return ArbitraryModint(*this) += p; } ArbitraryModint operator-(const ArbitraryModint &p) const{ return ArbitraryModint(*this) -= p; } ArbitraryModint operator*(const ArbitraryModint &p) const{ return ArbitraryModint(*this) *= p; } ArbitraryModint operator/(const ArbitraryModint &p) const { return ArbitraryModint(*this) /= p; } bool operator==(const ArbitraryModint &p) {return x == p.x;} bool operator!=(const ArbitraryModint &p) {return x != p.x;} ArbitraryModint inverse() const { int a = x,b = get_mod(),u = 1,v = 0,t; while(b > 0) { t = a / b; swap(a -= t * b,b); swap(u -= t * v,v); } return ArbitraryModint(u); } ArbitraryModint pow(int64_t n) const { ArbitraryModint ret(1),mul(x); while(n > 0) { if(n & 1) ret *= mul; mul *= mul; n >>= 1; } return ret; } friend ostream &operator<<(ostream &os,const ArbitraryModint &p) { return os << p.x; } friend istream &operator>>(istream &is,ArbitraryModint &a) { int64_t t; is >> t; a = ArbitraryModint(t); return (is); } int get() const {return x;} inline unsigned int rem(unsigned long long p) {return barrett().rem(p);}; static inline Barrett &barrett() { static Barrett b; return b; } static inline int &get_mod() { static int mod = 0; return mod; } static void set_mod(int md) { assert(0 < md && md <= (1LL << 30) - 1); get_mod() = md; barrett() = Barrett(md); } }; #line 556 "test.cpp" using mint = ArbitraryModint; int main() { LL(L,R); INT(m); arbitrary_mod_binomial C(m); mint::set_mod(m); mint ans; rep(i,L,R+1) { ans += C.C(2*i,i); } ans -= (R - L + 1) * 2; cout << ans << '\n'; }