#include using namespace std; using lint = long long int; using pint = pair; using plint = pair; struct fast_ios { fast_ios(){ cin.tie(0); ios::sync_with_stdio(false); cout << fixed << setprecision(20); }; } fast_ios_; #define ALL(x) (x).begin(), (x).end() #define SZ(x) ((lint)(x).size()) #define POW2(n) (1LL << (n)) #define FOR(i, begin, end) for(int i=(begin),i##_end_=(end);i=i##_begin_;i--) #define REP(i, n) FOR(i,0,n) #define IREP(i, n) IFOR(i,0,n) template void ndarray(vector &vec, int len) { vec.resize(len); } template void ndarray(vector &vec, int len, Args... args) { vec.resize(len); for (auto &v : vec) ndarray(v, args...); } template bool mmax(T &m, const T q) { if (m < q) {m = q; return true;} else return false; } template bool mmin(T &m, const T q) { if (m > q) {m = q; return true;} else return false; } template pair operator+(const pair &l, const pair &r) { return make_pair(l.first + r.first, l.second + r.second); } template pair operator-(const pair &l, const pair &r) { return make_pair(l.first - r.first, l.second - r.second); } template istream &operator>>(istream &is, vector &vec){ for (auto &v : vec) is >> v; return is; } ///// This part below is only for debug, not used ///// template ostream &operator<<(ostream &os, const vector &vec){ os << "["; for (auto v : vec) os << v << ","; os << "]"; return os; } template ostream &operator<<(ostream &os, const deque &vec){ os << "deq["; for (auto v : vec) os << v << ","; os << "]"; return os; } template ostream &operator<<(ostream &os, const set &vec){ os << "{"; for (auto v : vec) os << v << ","; os << "}"; return os; } template ostream &operator<<(ostream &os, const unordered_set &vec){ os << "{"; for (auto v : vec) os << v << ","; os << "}"; return os; } template ostream &operator<<(ostream &os, const multiset &vec){ os << "{"; for (auto v : vec) os << v << ","; os << "}"; return os; } template ostream &operator<<(ostream &os, const unordered_multiset &vec){ os << "{"; for (auto v : vec) os << v << ","; os << "}"; return os; } template ostream &operator<<(ostream &os, const pair &pa){ os << "(" << pa.first << "," << pa.second << ")"; return os; } template ostream &operator<<(ostream &os, const map &mp){ os << "{"; for (auto v : mp) os << v.first << "=>" << v.second << ","; os << "}"; return os; } template ostream &operator<<(ostream &os, const unordered_map &mp){ os << "{"; for (auto v : mp) os << v.first << "=>" << v.second << ","; os << "}"; return os; } #define dbg(x) cerr << #x << " = " << (x) << " (L" << __LINE__ << ") " << __FILE__ << endl; ///// END ///// /* #include #include #include using namespace __gnu_pbds; // find_by_order(), order_of_key() template using pbds_set = tree, rb_tree_tag, tree_order_statistics_node_update>; template using pbds_map = tree, rb_tree_tag, tree_order_statistics_node_update>; */ template struct ModInt { using lint = long long; static int get_mod() { return mod; } static int get_primitive_root() { static int primitive_root = 0; if (!primitive_root) { primitive_root = [&](){ std::set fac; int v = mod - 1; for (lint i = 2; i * i <= v; i++) while (v % i == 0) fac.insert(i), v /= i; if (v > 1) fac.insert(v); for (int g = 1; g < mod; g++) { bool ok = true; for (auto i : fac) if (ModInt(g).power((mod - 1) / i) == 1) { ok = false; break; } if (ok) return g; } return -1; }(); } return primitive_root; } int val; constexpr ModInt() : val(0) {} constexpr ModInt &_setval(lint v) { val = (v >= mod ? v - mod : v); return *this; } constexpr ModInt(lint v) { _setval(v % mod + mod); } explicit operator bool() const { return val != 0; } constexpr ModInt operator+(const ModInt &x) const { return ModInt()._setval((lint)val + x.val); } constexpr ModInt operator-(const ModInt &x) const { return ModInt()._setval((lint)val - x.val + mod); } constexpr ModInt operator*(const ModInt &x) const { return ModInt()._setval((lint)val * x.val % mod); } constexpr ModInt operator/(const ModInt &x) const { return ModInt()._setval((lint)val * x.inv() % mod); } constexpr ModInt operator-() const { return ModInt()._setval(mod - val); } constexpr ModInt &operator+=(const ModInt &x) { return *this = *this + x; } constexpr ModInt &operator-=(const ModInt &x) { return *this = *this - x; } constexpr ModInt &operator*=(const ModInt &x) { return *this = *this * x; } constexpr ModInt &operator/=(const ModInt &x) { return *this = *this / x; } friend constexpr ModInt operator+(lint a, const ModInt &x) { return ModInt()._setval(a % mod + x.val); } friend constexpr ModInt operator-(lint a, const ModInt &x) { return ModInt()._setval(a % mod - x.val + mod); } friend constexpr ModInt operator*(lint a, const ModInt &x) { return ModInt()._setval(a % mod * x.val % mod); } friend constexpr ModInt operator/(lint a, const ModInt &x) { return ModInt()._setval(a % mod * x.inv() % mod); } constexpr bool operator==(const ModInt &x) const { return val == x.val; } constexpr bool operator!=(const ModInt &x) const { return val != x.val; } bool operator<(const ModInt &x) const { return val < x.val; } // To use std::map friend std::istream &operator>>(std::istream &is, ModInt &x) { lint t; is >> t; x = ModInt(t); return is; } friend std::ostream &operator<<(std::ostream &os, const ModInt &x) { os << x.val; return os; } constexpr lint power(lint n) const { lint ans = 1, tmp = this->val; while (n) { if (n & 1) ans = ans * tmp % mod; tmp = tmp * tmp % mod; n /= 2; } return ans; } constexpr lint inv() const { return this->power(mod - 2); } constexpr ModInt operator^(lint n) const { return ModInt(this->power(n)); } constexpr ModInt &operator^=(lint n) { return *this = *this ^ n; } inline ModInt fac() const { static std::vector facs; int l0 = facs.size(); if (l0 > this->val) return facs[this->val]; facs.resize(this->val + 1); for (int i = l0; i <= this->val; i++) facs[i] = (i == 0 ? ModInt(1) : facs[i - 1] * ModInt(i)); return facs[this->val]; } ModInt doublefac() const { lint k = (this->val + 1) / 2; if (this->val & 1) return ModInt(k * 2).fac() / ModInt(2).power(k) / ModInt(k).fac(); else return ModInt(k).fac() * ModInt(2).power(k); } ModInt nCr(const ModInt &r) const { if (this->val < r.val) return ModInt(0); return this->fac() / ((*this - r).fac() * r.fac()); } ModInt sqrt() const { if (val == 0) return 0; if (mod == 2) return val; if (power((mod - 1) / 2) != 1) return 0; ModInt b = 1; while (b.power((mod - 1) / 2) == 1) b += 1; int e = 0, m = mod - 1; while (m % 2 == 0) m >>= 1, e++; ModInt x = power((m - 1) / 2), y = (*this) * x * x; x *= (*this); ModInt z = b.power(m); while (y != 1) { int j = 0; ModInt t = y; while (t != 1) j++, t *= t; z = z.power(1LL << (e - j - 1)); x *= z, z *= z, y *= z; e = j; } return ModInt(std::min(x.val, mod - x.val)); } }; constexpr int MOD = 1000000007; using mint = ModInt; template struct matrix { int H, W; std::vector elem; typename std::vector::iterator operator[](int i) { return elem.begin() + i * W; } inline T &at(int i, int j) { return elem[i * W + j]; } inline T get(int i, int j) const { return elem[i * W + j]; } operator std::vector>() const { std::vector> ret(H); for (int i = 0; i < H; i++) std::copy(elem.begin() + i * W, elem.begin() + (i + 1) * W, std::back_inserter(ret[i])); return ret; } matrix(int H = 0, int W = 0) : H(H), W(W), elem(H * W) {} matrix(const std::vector> &d) : H(d.size()), W(d.size() ? d[0].size() : 0) { for (auto &raw : d) std::copy(raw.begin(), raw.end(), std::back_inserter(elem)); } static matrix Identity(int N) { matrix ret(N, N); for (int i = 0; i < N; i++) ret.at(i, i) = 1; return ret; } matrix operator-() const { matrix ret(H, W); for (int i = 0; i < H * W; i++) ret.elem[i] = -elem[i]; return ret; } matrix operator+(const matrix &r) const { matrix ret(H, W); for (int i = 0; i < H * W; i++) ret.elem[i] += r.elem[i]; return ret; } matrix operator-(const matrix &r) const { matrix ret(H, W); for (int i = 0; i < H * W; i++) ret.elem[i] -= r.elem[i]; return ret; } matrix operator*(const matrix &r) const { matrix ret(H, r.W); for (int i = 0; i < H; i++) { for (int k = 0; k < W; k++) { for (int j = 0; j < r.W; j++) { ret.at(i, j) += this->get(i, k) * r.get(k, j); } } } return ret; } matrix &operator+=(const matrix &r) { return *this = *this + r; } matrix &operator-=(const matrix &r) { return *this = *this - r; } matrix &operator*=(const matrix &r) { return *this = *this * r; } bool operator==(const matrix &r) const { return H == r.H and W == r.W and elem == r.elem; } bool operator!=(const matrix &r) const { return H != r.H or W != r.W or elem != r.elem; } bool operator<(const matrix &r) const { return elem < r.elem; } matrix pow(int64_t n) const { matrix ret = Identity(H); if (n == 0) return ret; for (int i = 63 - __builtin_clzll(n); i >= 0; i--) { ret *= ret; if ((n >> i) & 1) ret *= (*this); } return ret; } matrix transpose() const { matrix ret(W, H); for (int i = 0; i < H; i++) for (int j = 0; j < W; j++) ret.at(j, i) = this->get(i, j); return ret; } // Gauss-Jordan elimination // - Require inverse for every non-zero element // - Complexity: O(H^2 W) matrix gauss_jordan() const { int c = 0; matrix mtr(*this); for (int h = 0; h < H; h++) { if (c == W) break; int piv = -1; for (int j = h; j < H; j++) if (mtr.get(j, c)) { piv = j; break; } if (piv == -1) { c++; h--; continue; } if (h != piv) { for (int w = 0; w < W; w++) { std::swap(mtr[piv][w], mtr[h][w]); mtr.at(piv, w) *= -1; // To preserve sign of determinant } } for (int hh = 0; hh < H; hh++) if (hh != h) { T coeff = mtr.at(hh, c) * mtr.at(h, c).inv(); for (int w = W - 1; w >= c; w--) { mtr.at(hh, w) -= mtr.at(h, w) * coeff; } } c++; } return mtr; } int rank_of_gauss_jordan() const { for (int i = H * W - 1; i >= 0; i--) if (elem[i]) return i / W + 1; return 0; } T determinant_of_upper_triangle() const { T ret = 1; for (int i = 0; i < H; i++) ret *= get(i, i); return ret; } friend std::ostream &operator<<(std::ostream &os, const matrix &x) { os << "[(" << x.H << " * " << x.W << " matrix)"; for (int i = 0; i < x.H; i++) { os << "\n["; for (int j = 0; j < x.W; j++) os << x.get(i, j) << ","; os << "]"; } os << "]\n"; return os; } friend std::istream &operator>>(std::istream &is, matrix &x) { for (auto &v : x.elem) is >> v; return is; } }; int main() { int N, P; cin >> N >> P; vector A(N + 10); A[2] = 1; FOR(i, 3, N + 1) A[i] = A[i - 1] * P + A[i - 2]; vector AA = A; REP(i, N + 1) AA[i + 1] += AA[i]; mint ret = 0; FOR(i, 1, N + 1) ret += A[i] * AA[i]; cout << ret << endl; }