#define _USE_MATH_DEFINES #include using namespace std; template class Modular { private: long long value; constexpr static int MOD() { return static_cast(T::value); } public: constexpr Modular() : value() {}; constexpr Modular(const Modular& other) : value(other.value) {} template constexpr Modular(const U& x) { value = normalize(x); } template static long long normalize(const U& x) { long long v; if (-MOD() <= x && x < MOD()) v = static_cast(x); else v = static_cast(x % MOD()); if (v < 0) v += MOD(); return v; } constexpr static long long inverse(long long x) { x = (x % MOD() + MOD()) % MOD(); long long y = MOD(), u = 1, v = 0; while(y) { long long t = x / y; x -= t * y; swap(x, y); u -= t * v; swap(u, v); } return (u % MOD() + MOD()) % MOD(); } static long long mul(const long long& a, const long long& b) { long long res; #ifdef _WIN32 unsigned long long x = a * b; unsigned xh = (unsigned) (x >> 32), xl = (unsigned) x, d, m; asm( "divl %4; \n\t" : "=a" (d), "=d" (m) : "d" (xh), "a" (xl), "r" (MOD()) ); res = m; #else res = a * b % MOD(); #endif return res; } explicit operator long long() const noexcept { return value;} template explicit operator U() const noexcept { return static_cast(value); } constexpr Modular& operator=(const Modular& other) & noexcept { value = other.value; return *this; } template constexpr Modular& operator=(const U& other) & noexcept { return *this = Modular(other); } constexpr Modular& operator+=(const Modular& other) noexcept { if ((value += other.value) >= MOD()) value -= MOD(); return *this; } template constexpr Modular& operator+=(const U& other) noexcept { return *this += Modular(other); } constexpr Modular& operator-=(const Modular& other) noexcept { if ((value -= other.value) < 0) value += MOD(); return *this; } template constexpr Modular& operator-=(const U& other) noexcept { return *this -= Modular(other); } constexpr Modular& operator*=(const Modular& other) noexcept { this->value = mul(this->value, other.value); return *this; } template constexpr Modular& operator*=(const U& other) noexcept {return *this *= Modular(other); } constexpr Modular& operator/=(const Modular& other) noexcept { return *this *= Modular(inverse(other.value)); } template constexpr Modular& operator/=(const U& other) noexcept { return *this *= Modular(inverse(normalize(other))); } constexpr Modular& operator++() noexcept {return *this += 1; } constexpr Modular operator++(int) noexcept { Modular ret(*this); *this += 1; return ret; } constexpr Modular& operator--() noexcept {return *this -= 1; } constexpr Modular operator--(int) noexcept { Modular ret(*this); *this -= 1; return ret; } constexpr Modular operator-() const { return Modular(-value); } friend constexpr bool operator==(const Modular& lhs, const Modular& rhs) noexcept { return lhs.value == rhs.value; } template friend constexpr bool operator==(const Modular& lhs, U rhs) noexcept { return lhs == Modular(rhs); } template friend constexpr bool operator==(U lhs, const Modular& rhs) noexcept { return Modular(lhs) == rhs; } friend constexpr bool operator!=(const Modular& lhs, const Modular& rhs) noexcept { return !(lhs == rhs); } template friend constexpr bool operator!=(const Modular& lhs, U rhs) noexcept { return !(lhs == rhs); } template friend constexpr bool operator!=(U lhs, const Modular rhs) noexcept { return !(lhs == rhs); } friend constexpr bool operator<(const Modular& lhs, const Modular& rhs) noexcept { return lhs.value < rhs.value; } template friend constexpr bool operator<(const Modular &lhs, U rhs) noexcept { return lhs.value < rhs; } template friend constexpr bool operator<(U lhs, const Modular &rhs) noexcept { return lhs < rhs.value; } friend constexpr bool operator>(const Modular& lhs, const Modular& rhs) noexcept { return rhs.value < lhs.value; } template friend constexpr bool operator>(const Modular &lhs, U rhs) noexcept { return rhs.value < lhs; } template friend constexpr bool operator>(U lhs, const Modular &rhs) noexcept { return rhs < lhs.value; } friend constexpr bool operator<=(const Modular& lhs, const Modular& rhs) noexcept { return !(lhs.value > rhs.value); } template friend constexpr bool operator<=(const Modular &lhs, U rhs) noexcept { return !(lhs.value > rhs); } template friend constexpr bool operator<=(U lhs, const Modular &rhs) noexcept { return !(lhs < rhs.value); } friend constexpr bool operator>=(const Modular& lhs, const Modular& rhs) noexcept { return !(lhs.value < rhs.value); } template friend constexpr bool operator>=(const Modular &lhs, U rhs) noexcept { return !(lhs.value < rhs); } template friend constexpr bool operator>=(U lhs, const Modular &rhs) noexcept { return !(lhs < rhs.value); } friend constexpr Modular operator+(const Modular& lhs, const Modular& rhs) noexcept { return Modular(lhs) += rhs; } template friend constexpr Modular operator+(const Modular& lhs, U rhs) noexcept { return Modular(lhs) += rhs; } template friend constexpr Modular operator+(U lhs, const Modular &rhs) noexcept { return Modular(lhs) += rhs; } friend constexpr Modular operator-(const Modular& lhs, const Modular& rhs) noexcept { return Modular(lhs) -= rhs; } template friend constexpr Modular operator-(const Modular& lhs, U rhs) noexcept { return Modular(lhs) -= rhs; } template friend constexpr Modular operator-(U lhs, const Modular &rhs) noexcept { return Modular(lhs) -= rhs; } friend constexpr Modular operator*(const Modular& lhs, const Modular& rhs) noexcept { return Modular(lhs) *= rhs; } template friend constexpr Modular operator*(const Modular& lhs, U rhs) noexcept { return Modular(lhs) *= rhs; } template friend constexpr Modular operator*(U lhs, const Modular &rhs) noexcept { return Modular(lhs) *= rhs; } friend constexpr Modular operator/(const Modular& lhs, const Modular& rhs) noexcept { return Modular(lhs) /= rhs; } template friend constexpr Modular operator/(const Modular& lhs, U rhs) noexcept { return Modular(lhs) /= rhs; } template friend constexpr Modular operator/(U lhs, const Modular &rhs) noexcept { return Modular(lhs) /= rhs; } friend std::ostream& operator<<(std::ostream& stream, const Modular& number) noexcept { return stream << number.value; } friend std::istream& operator>>(std::istream& stream, Modular& number) { long long in; stream >> in; number.value = Modular::normalize(in); return stream; } constexpr int getmod() const { return MOD(); } }; template Modular power(const Modular& x, const U& y) { assert(y >= 0); Modular k = x, result = 1; U p = y; while (p > 0) { if (p & 1) result *= k; k *= k; p >>= 1; } return result; } template class BinaryCoefficients { private: vector> fact_, inv_, finv_; long long MOD = static_cast(T::value); public: constexpr BinaryCoefficients(int n = 2020200) : fact_(n, 1), inv_(n, 1), finv_(n, 1) { for (int i = 2; i < n; i++) { fact_[i] = fact_[i - 1] * i; inv_[i] = -inv_[MOD % i] * (MOD / i); finv_[i] = finv_[i - 1] * inv_[i]; } } constexpr Modular comb(int n, int k) const noexcept { if (n < k || n < 0 || k < 0) return 0; return fact_[n] * finv_[k] * finv_[n - k]; } constexpr Modular fact(int n) const noexcept { if (n < 0) return 0; return fact_[n]; } constexpr Modular inv(int n) const noexcept { if (n < 0) return 0; return inv_[n]; } constexpr Modular finv(int n) const noexcept { if (n < 0) return 0; return finv_[n]; } }; constexpr int mod = 1e9 + 7; //constexpr int mod = 998244353; using mint = Modular::type, mod>>; using bicoef = BinaryCoefficients::type, mod>>; // struct modValue { static int value; }; // int modValue::value; // int& mod = modValue::value; // using mint = Modular; // using bicoef = BinaryCoefficients; template class Matrix { private: vector> matrix; template using ET = enable_if::value>; template using EF = enable_if::value>; template::type* = nullptr> static constexpr bool is_zero (const U& x) { return abs(x) < 1e-8; } template::type* = nullptr> static constexpr bool is_zero (const U& x) { return x == U(0); } public: constexpr Matrix () {} constexpr Matrix (int h, int w) : matrix(vector>(h, vector(w))) {} constexpr Matrix (int h, int w, T val) : matrix(vector>(h, vector(w, val))) {} constexpr Matrix (const vector>& mat) : matrix(mat) {} constexpr Matrix (const Matrix& mat) : matrix(mat.matrix) {} constexpr size_t height () const noexcept { return matrix.size(); } constexpr size_t width () const noexcept { assert(!empty()); return matrix[0].size(); } constexpr bool empty() const noexcept { return matrix.empty(); } vector& operator[] (size_t row) { assert(matrix.size() > row); return matrix[row]; } const vector& operator[] (size_t row) const { assert(matrix.size() > row); return matrix[row]; } static Matrix identity (int n) { Matrix res(n, n); for (int i = 0; i < n; ++i) res[i][i] = T(1); return res; } Matrix identity () { assert(height() == width()); return identity(height()); }; constexpr Matrix& operator= (const Matrix& lhs) & noexcept { //int h = lhs.matrix.size(); // assert(!lhs.matrix.empty()); matrix = lhs.matrix; return *this; // int w = lhs.matrix[0].size(); // matrix = vector>(h, vector(w, T())); // for (int i = 0; i < h; i++) for (int j = 0; j < w; j++) matrix[i][j] = lhs.matrix[i][j]; // return *this; } constexpr Matrix& operator= (const vector>& lhs) & noexcept { return *this = Matrix(lhs); } constexpr Matrix& operator+= (const Matrix& lhs) noexcept { assert(height() == lhs.matrix.size()); assert(width() == lhs.matrix[0].sizse()); for (int i = 0; i < height(); ++i) for (int j = 0; j < width(); ++j) matrix[i][j] += lhs[i][j]; return (*this); } constexpr Matrix& operator+= (const vector>& lhs) noexcept { return *this += Matrix(lhs); } constexpr Matrix& operator-= (const Matrix& lhs) noexcept { assert(height() == lhs.matrix.size()); assert(width() == lhs.matrix[0].sizse()); for (int i = 0; i < height(); ++i) for (int j = 0; j < width(); ++j) matrix[i][j] -= lhs[i][j]; return (*this); } constexpr Matrix& operator-= (const vector>& lhs) noexcept { return *this -= Matrix(lhs); } constexpr Matrix& operator*= (const Matrix& lhs) noexcept { Matrix res(height(), lhs[0].size()); for (int i = 0; i < (int) height(); ++i) for (int j = 0; j < (int) lhs[0].size(); ++j) for (int k = 0; k < (int) width(); k++) { res[i][j] += matrix[i][k] * lhs[k][j]; } matrix.swap(res.matrix); return (*this); } constexpr Matrix& operator*= (const vector>& lhs) noexcept { return *this *= Matrix(lhs); } friend constexpr bool operator==(const Matrix& lhs, const Matrix& rhs) noexcept { return lhs.matrix == rhs.matrix; } friend constexpr bool operator==(const Matrix& lhs, const vector>& rhs) noexcept { return lhs == Matrix(rhs); } friend constexpr bool operator==(const vector>& lhs, const Matrix& rhs) noexcept { return Matrix(lhs) == rhs; } friend constexpr Matrix operator+(const Matrix& lhs, const Matrix& rhs) noexcept { return Matrix(lhs) += rhs; } friend constexpr Matrix operator+(const Matrix& lhs, const vector>& rhs) noexcept { return Matrix(lhs) += rhs; } friend constexpr Matrix operator+(const vector>& lhs, const Matrix& rhs) noexcept { return Matrix(lhs) += rhs; } friend constexpr Matrix operator-(const Matrix& lhs, const Matrix& rhs) noexcept { return Matrix(lhs) -= rhs; } friend constexpr Matrix operator-(const Matrix& lhs, const vector>& rhs) noexcept { return Matrix(lhs) -= rhs; } friend constexpr Matrix operator-(const vector>& lhs, const Matrix& rhs) noexcept { return Matrix(lhs) -= rhs; } friend constexpr Matrix operator*(const Matrix& lhs, const Matrix& rhs) noexcept { return Matrix(lhs) *= rhs; } friend constexpr Matrix operator*(const Matrix& lhs, const vector>& rhs) noexcept { return Matrix(lhs) *= rhs; } friend constexpr Matrix operator*(const vector>& lhs, const Matrix& rhs) noexcept { return Matrix(lhs) *= rhs; } template Matrix power(U n) { Matrix x(*this), res = identity(height()); while (n) { if (n & 1) res *= x; x *= x; n >>= 1; } return res; } T determinant() { Matrix a(*this); assert(a.height() == a.width()); T res = 1; for (int i = 0; i < width(); ++i) { int pivot = -1; for (int j = i; j < width(); ++j) if (!is_zero(a[j][i])) pivot = j; if (pivot == -1) return T(0); if (i != pivot) { res *= -1; swap(a[i], a[pivot]); } res *= a[i][i]; T div = a[i][i]; for (int j = 0; j < width(); ++j) a[i][j] /= div; for (int j = i + 1; j < width(); ++j) { T b = a[j][i]; for (int k = 0; k < width(); ++k) { a[j][k] -= a[i][k] * b; } } } return res; } }; signed main() { ios::sync_with_stdio(false); cin.tie(0); int m, k; cin >> m >> k; Matrix mul(m, m); for (int from = 0; from < m; from++) { for (int x = 0; x < m; x++) { int res = (from + x) % m; mul[res][from]++; res = (from * x) % m; mul[res][from]++; } } Matrix mat(m, 1); mat[0][0] = 1; mul = mul.power(k); auto ans = mul * mat; cout << ans[0][0] << endl; return 0; }