#line 2 "template/template.hpp" using namespace std; #include #line 1 "template/inout.hpp" namespace noya2 { template ostream &operator<<(ostream &os, const pair &p){ os << p.first << " " << p.second; return os; } template istream &operator>>(istream &is, pair &p){ is >> p.first >> p.second; return is; } template ostream &operator<<(ostream &os, const vector &v){ int s = (int)v.size(); for (int i = 0; i < s; i++) os << (i ? " " : "") << v[i]; return os; } template istream &operator>>(istream &is, vector &v){ for (auto &x : v) is >> x; return is; } void in() {} template void in(T &t, U &...u){ cin >> t; in(u...); } void out() { cout << "\n"; } template void out(const T &t, const U &...u){ cout << t; if (sizeof...(u)) cout << sep; out(u...); } template void out(const vector> &vv){ int s = (int)vv.size(); for (int i = 0; i < s; i++) out(vv[i]); } struct IoSetup { IoSetup(){ cin.tie(nullptr); ios::sync_with_stdio(false); cout << fixed << setprecision(15); cerr << fixed << setprecision(7); } } iosetup_noya2; } // namespace noya2 #line 1 "template/const.hpp" namespace noya2{ const int iinf = 1'000'000'007; const long long linf = 2'000'000'000'000'000'000LL; const long long mod998 = 998244353; const long long mod107 = 1000000007; const long double pi = 3.14159265358979323; const vector dx = {0,1,0,-1,1,1,-1,-1}; const vector dy = {1,0,-1,0,1,-1,-1,1}; const string ALP = "ABCDEFGHIJKLMNOPQRSTUVWXYZ"; const string alp = "abcdefghijklmnopqrstuvwxyz"; const string NUM = "0123456789"; void yes(){ cout << "Yes\n"; } void no(){ cout << "No\n"; } void YES(){ cout << "YES\n"; } void NO(){ cout << "NO\n"; } void yn(bool t){ t ? yes() : no(); } void YN(bool t){ t ? YES() : NO(); } } // namespace noya2 #line 1 "template/utils.hpp" namespace noya2{ unsigned long long inner_binary_gcd(unsigned long long a, unsigned long long b){ if (a == 0 || b == 0) return a + b; int n = __builtin_ctzll(a); int m = __builtin_ctzll(b); a >>= n; b >>= m; while (a != b) { int m = __builtin_ctzll(a - b); bool f = a > b; unsigned long long c = f ? a : b; b = f ? b : a; a = (c - b) >> m; } return a << min(n, m); } template T gcd_fast(T a, T b){ return static_cast(inner_binary_gcd(abs(a),abs(b))); } template T floor_div(const T n, const T d) { assert(d != 0); return n / d - static_cast((n ^ d) < 0 && n % d != 0); } template T ceil_div(const T n, const T d) { assert(d != 0); return n / d + static_cast((n ^ d) >= 0 && n % d != 0); } template void uniq(vector &v){ sort(all(v)); v.erase(unique(all(v)),v.end()); } template inline bool chmin(T &x, U y) { return (y < x) ? (x = y, true) : false; } template inline bool chmax(T &x, U y) { return (x < y) ? (x = y, true) : false; } template inline bool range(T l, T x, T r){ return l <= x && x < r; } } // namespace noya2 #line 8 "template/template.hpp" #define rep(i,n) for (int i = 0; i < (int)(n); i++) #define repp(i,m,n) for (int i = (m); i < (int)(n); i++) #define reb(i,n) for (int i = (int)(n-1); i >= 0; i--) #define all(v) (v).begin(),(v).end() using ll = long long; using ld = long double; using uint = unsigned int; using ull = unsigned long long; using pii = pair; using pll = pair; using pil = pair; using pli = pair; namespace noya2{ /* ~ (. _________ . /) */ } using namespace noya2; #line 2 "c.cpp" #line 2 "utility/modint.hpp" // AtCoderLibrary をそのままパクっている なにもわかっていない // \( x _______ x) ~ #line 8 "utility/modint.hpp" #include #line 10 "utility/modint.hpp" namespace noya2 { constexpr long long safe_mod(long long x, long long m) { x %= m; if (x < 0) x += m; return x; } struct barrett { unsigned int _m; unsigned long long im; explicit barrett(unsigned int m) : _m(m), im((unsigned long long)(-1) / m + 1) {} unsigned int umod() const { return _m; } unsigned int mul(unsigned int a, unsigned int b) const { 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; } }; 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; } 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}; 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; auto tmp = s; s = t; t = tmp; tmp = m0; m0 = m1; m1 = tmp; } if (m0 < 0) m0 += b / s; return {s, m0}; } 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 noya2 namespace noya2 { #ifndef _MSC_VER template using is_signed_int128 = typename std::conditional::value || std::is_same::value, std::true_type, std::false_type>::type; template using is_unsigned_int128 = typename std::conditional::value || std::is_same::value, std::true_type, std::false_type>::type; template using make_unsigned_int128 = typename std::conditional::value, __uint128_t, unsigned __int128>; template using is_integral = typename std::conditional::value || is_signed_int128::value || is_unsigned_int128::value, std::true_type, std::false_type>::type; template using is_signed_int = typename std::conditional<(is_integral::value && std::is_signed::value) || is_signed_int128::value, std::true_type, std::false_type>::type; template using is_unsigned_int = typename std::conditional<(is_integral::value && std::is_unsigned::value) || is_unsigned_int128::value, std::true_type, std::false_type>::type; template using to_unsigned = typename std::conditional::value, make_unsigned_int128, typename std::conditional::value, std::make_unsigned, std::common_type>::type>::type; #else template using is_integral = typename std::is_integral; template using is_signed_int = typename std::conditional::value && std::is_signed::value, std::true_type, std::false_type>::type; template using is_unsigned_int = typename std::conditional::value && std::is_unsigned::value, std::true_type, std::false_type>::type; template using to_unsigned = typename std::conditional::value, std::make_unsigned, std::common_type>::type; #endif template using is_signed_int_t = std::enable_if_t::value>; template using is_unsigned_int_t = std::enable_if_t::value>; template using to_unsigned_t = typename to_unsigned::type; } // namespace noya2 namespace noya2 { struct modint_base {}; struct static_modint_base : modint_base {}; template using is_modint = std::is_base_of; template using is_modint_t = std::enable_if_t::value>; } // namespace noya2 template * = nullptr> struct static_modint : noya2::static_modint_base { using mint = static_modint; public: static constexpr int mod() { return m; } static mint raw(int v) { mint x; x._v = v; return x; } static_modint() : _v(0) {} template * = nullptr> static_modint(T v) { long long x = (long long)(v % (long long)(umod())); if (x < 0) x += umod(); _v = (unsigned int)(x); } template * = nullptr> static_modint(T v) { _v = (unsigned int)(v % umod()); } unsigned int val() const { return _v; } mint& operator++() { _v++; if (_v == umod()) _v = 0; return *this; } mint& operator--() { if (_v == 0) _v = umod(); _v--; return *this; } mint operator++(int) { mint result = *this; ++*this; return result; } mint operator--(int) { mint result = *this; --*this; return result; } mint& operator+=(const mint& rhs) { _v += rhs._v; if (_v >= umod()) _v -= umod(); return *this; } mint& operator-=(const mint& rhs) { _v -= rhs._v; if (_v >= umod()) _v += umod(); return *this; } mint& operator*=(const mint& rhs) { unsigned long long z = _v; z *= rhs._v; _v = (unsigned int)(z % umod()); return *this; } mint& operator/=(const mint& rhs) { return *this = *this * rhs.inv(); } mint operator+() const { return *this; } mint operator-() const { return mint() - *this; } mint pow(long long n) const { assert(0 <= n); mint x = *this, r = 1; while (n) { if (n & 1) r *= x; x *= x; n >>= 1; } return r; } mint inv() const { if (prime) { assert(_v); return pow(umod() - 2); } else { auto eg = noya2::inv_gcd(_v, m); assert(eg.first == 1); return eg.second; } } friend mint operator+(const mint& lhs, const mint& rhs) { return mint(lhs) += rhs; } friend mint operator-(const mint& lhs, const mint& rhs) { return mint(lhs) -= rhs; } friend mint operator*(const mint& lhs, const mint& rhs) { return mint(lhs) *= rhs; } friend mint operator/(const mint& lhs, const mint& rhs) { return mint(lhs) /= rhs; } friend bool operator==(const mint& lhs, const mint& rhs) { return lhs._v == rhs._v; } friend bool operator!=(const mint& lhs, const mint& rhs) { return lhs._v != rhs._v; } friend std::ostream &operator<<(std::ostream &os, const mint& p) { return os << p.val(); } friend std::istream &operator>>(std::istream &is, mint &a) { long long t; is >> t; a = mint(t); return (is); } private: unsigned int _v; static constexpr unsigned int umod() { return m; } static constexpr bool prime = noya2::is_prime; }; template struct dynamic_modint : noya2::modint_base { using mint = dynamic_modint; public: static int mod() { return (int)(bt.umod()); } static void set_mod(int m) { assert(1 <= m); bt = noya2::barrett(m); } static mint raw(int v) { mint x; x._v = v; return x; } dynamic_modint() : _v(0) {} template * = nullptr> dynamic_modint(T v) { long long x = (long long)(v % (long long)(mod())); if (x < 0) x += mod(); _v = (unsigned int)(x); } template * = nullptr> dynamic_modint(T v) { _v = (unsigned int)(v % mod()); } unsigned int val() const { return _v; } mint& operator++() { _v++; if (_v == umod()) _v = 0; return *this; } mint& operator--() { if (_v == 0) _v = umod(); _v--; return *this; } mint operator++(int) { mint result = *this; ++*this; return result; } mint operator--(int) { mint result = *this; --*this; return result; } mint& operator+=(const mint& rhs) { _v += rhs._v; if (_v >= umod()) _v -= umod(); return *this; } mint& operator-=(const mint& rhs) { _v += mod() - rhs._v; if (_v >= umod()) _v -= umod(); return *this; } mint& operator*=(const mint& rhs) { _v = bt.mul(_v, rhs._v); return *this; } mint& operator/=(const mint& rhs) { return *this = *this * rhs.inv(); } mint operator+() const { return *this; } mint operator-() const { return mint() - *this; } mint pow(long long n) const { assert(0 <= n); mint x = *this, r = 1; while (n) { if (n & 1) r *= x; x *= x; n >>= 1; } return r; } mint inv() const { auto eg = noya2::inv_gcd(_v, mod()); assert(eg.first == 1); return eg.second; } friend mint operator+(const mint& lhs, const mint& rhs) { return mint(lhs) += rhs; } friend mint operator-(const mint& lhs, const mint& rhs) { return mint(lhs) -= rhs; } friend mint operator*(const mint& lhs, const mint& rhs) { return mint(lhs) *= rhs; } friend mint operator/(const mint& lhs, const mint& rhs) { return mint(lhs) /= rhs; } friend bool operator==(const mint& lhs, const mint& rhs) { return lhs._v == rhs._v; } friend bool operator!=(const mint& lhs, const mint& rhs) { return lhs._v != rhs._v; } friend std::ostream &operator<<(std::ostream &os, const mint& p) { return os << p.val(); } friend std::istream &operator>>(std::istream &is, mint &a) { long long t; is >> t; a = mint(t); return (is); } private: unsigned int _v; static noya2::barrett bt; static unsigned int umod() { return bt.umod(); } }; template noya2::barrett dynamic_modint::bt(998244353); using modint998244353 = static_modint<998244353>; using modint1000000007 = static_modint<1000000007>; using modint = dynamic_modint<-1>; namespace noya2 { template using is_static_modint = std::is_base_of; template using is_static_modint_t = std::enable_if_t::value>; template struct is_dynamic_modint : public std::false_type {}; template struct is_dynamic_modint> : public std::true_type {}; template using is_dynamic_modint_t = std::enable_if_t::value>; } // namespace noya2 #line 4 "c.cpp" using mint = modint; #line 2 "math/matrix.hpp" #line 4 "math/matrix.hpp" namespace noya2{ template struct Matrix{ int rows; int cols; vector> m; Matrix (int h = 0, int w = -1, T init = T(0)) : m(h,vector((w == -1 ? h : w),init)){ rows = h, cols = (w == -1 ? h : w); } Matrix (vector> _init) : m(_init), rows(_init.size()), cols(_init.at(0).size()){} vector& operator[](const int i) const {return m[i];} vector& operator[](const int i) {return m[i];} Matrix &operator+= (const Matrix &r){ assert(this->rows == r.rows && this->cols == r.cols); for (int i = 0; i < r.rows; ++i){ for (int j = 0; j < r.cols; ++j){ m[i][j] += r.m[i][j]; } } return *this; } Matrix &operator-= (const Matrix &r){ assert(this->rows == r.rows && this->cols == r.cols); for (int i = 0; i < r.rows; ++i){ for (int j = 0; j < r.cols; ++j){ m[i][j] -= r.m[i][j]; } } return *this; } Matrix &operator*= (const Matrix &r){ assert(this->cols == r.rows); Matrix res(rows, r.cols); for (int i = 0; i < rows; ++i){ for (int j = 0; j < r.cols; ++j){ for (int k = 0; k < r.rows; ++k){ res[i][j] += m[i][k] * r.m[k][j]; } } } return *this = res; } Matrix operator+ (const Matrix &r) const {return Matrix(*this) += r;} Matrix operator- (const Matrix &r) const {return Matrix(*this) -= r;} Matrix operator* (const Matrix &r) const {return Matrix(*this) *= r;} bool operator== (const Matrix &r){ if (rows != r.rows || cols != r.cols) return false; for (int i = 0; i < r.rows; ++i){ for (int j = 0; j < r.cols; ++j){ if (m[i][j] != r.m[i][j]) return false; } } return true; } Matrix& operator+=(const T &r){ for (int i = 0; i < rows; ++i){ for (int j = 0; j < cols; ++j){ m[i][j] += r; } } return *this; } Matrix& operator-=(const T &r){ for (int i = 0; i < rows; ++i){ for (int j = 0; j < cols; ++j){ m[i][j] -= r; } } return *this; } Matrix& operator*=(const T &r){ for (int i = 0; i < rows; ++i){ for (int j = 0; j < cols; ++j){ m[i][j] *= r; } } return *this; } Matrix& operator/=(const T &r){ for (int i = 0; i < rows; ++i){ for (int j = 0; j < cols; ++j){ m[i][j] /= r; } } return *this; } Matrix operator+ (const T &r) const {return Matrix(*this) += r;} Matrix operator- (const T &r) const {return Matrix(*this) -= r;} Matrix operator* (const T &r) const {return Matrix(*this) *= r;} Matrix operator/ (const T &r) const {return Matrix(*this) /= r;} Matrix e(){ assert(this->rows == this->cols); Matrix res(this->rows, this->rows); for (int i = 0; i < rows; ++i) res[i][i] = 1; return res; } Matrix pow(long long n){ assert(this->rows == this->cols); if (n == 0) return e(); Matrix f = pow(n / 2); Matrix ans = f * f; if (n % 2 == 1) ans *= *this; return ans; } // for T = int, long long, double, long double void show(){ for (int i = 0; i < rows; ++i){ for (int j = 0; j < cols; ++j){ cout << m[i][j] << (j+1 == this->cols ? "\n" : " "); } } } T determinant() const { Matrix B(*this); assert(rows == cols); T ret = 1; for (int i = 0; i < rows; i++) { int idx = -1; for (int j = i; j < cols; j++) { if (B[j][i] != 0) { idx = j; break; } } if (idx == -1) return 0; if (i != idx) { ret *= T(-1); swap(B[i], B[idx]); } ret *= B[i][i]; T inv = T(1) / B[i][i]; for (int j = 0; j < cols; j++) { B[i][j] *= inv; } for (int j = i + 1; j < rows; j++) { T a = B[j][i]; if (a == 0) continue; for (int k = i; k < cols; k++) { B[j][k] -= B[i][k] * a; } } } return ret; } }; } // namespace noya2 #line 2 "data_structure/fenwick_tree.hpp" #line 4 "data_structure/fenwick_tree.hpp" namespace noya2{ template struct fenwick_tree { public: fenwick_tree() : _n(0) {} explicit fenwick_tree(int n) : _n(n), data(n) {} void add(int p, T x) { assert(0 <= p && p < _n); p++; while (p <= _n) { data[p - 1] += x; p += p & -p; } } T sum(int l, int r) { assert(0 <= l && l <= r && r <= _n); return sum(r) - sum(l); } private: int _n; vector data; T sum(int r) { T s = 0; while (r > 0) { s += data[r - 1]; r -= r & -r; } return s; } }; } // namespace noya2 #line 7 "c.cpp" vector> _coef = { {1,0,0,0,1}, {0,3,2,2,0}, {0,0,3,0,0}, {0,0,3,3,0}, {0,0,0,0,1}, }; void solve(){ int n, b, q; in(n,b,q); mint::set_mod(b); fenwick_tree fen(n+1); Matrix coef(5); rep(i,5) rep(j,5) coef[i][j] = _coef[i][j]; vector cnt(q); rep(i,q){ int l, m, r; in(l,m,r); l--, m--; fen.add(l,1); fen.add(r,-1); cnt[i] = fen.sum(0,m+1); } vector> ids(q+1); rep(i,q) ids[cnt[i]].emplace_back(i); auto cur = coef.e(); Matrix one(5,1,1); vector> ans(q,vector(3)); rep(t,q+1){ auto tmp = cur * one; for (int i : ids[t]){ rep(k,3) ans[i][k] = tmp[k][0]; } cur *= coef; } rep(i,q) out(ans[i]); } int main(){ int t = 1; //in(t); while (t--) { solve(); } }