#include "bits/stdc++.h" #pragma GCC optimize("Ofast") // Begin Header {{{ using namespace std; #ifndef DEBUG #define dump(...) #endif #define all(x) x.begin(), x.end() #define rep(i, n) for (intmax_t i = 0, i##_limit = (n); i < i##_limit; ++i) #define reps(i, b, e) for (intmax_t i = (b), i##_limit = (e); i <= i##_limit; ++i) #define repr(i, b, e) for (intmax_t i = (b), i##_limit = (e); i >= i##_limit; --i) #define var(Type, ...) Type __VA_ARGS__; input(__VA_ARGS__) constexpr size_t operator""_zu(unsigned long long value) { return value; }; constexpr intmax_t operator""_jd(unsigned long long value) { return value; }; constexpr uintmax_t operator""_ju(unsigned long long value) { return value; }; constexpr int INF = 0x3f3f3f3f; constexpr intmax_t LINF = 0x3f3f3f3f3f3f3f3f_jd; template using MaxHeap = priority_queue, less>; template using MinHeap = priority_queue, greater>; inline void input() {} template inline void input(Head&& head, Tail&&... tail) { cin >> head; input(forward(tail)...); } template inline void input(vector &vec) { for (auto &e: vec) { cin >> e; } } template inline void input(vector> &mat) { for (auto &vec: mat) { input(vec); } } inline void print() { cout << "\n"; } template inline void print(Head&& head, Tail&&... tail) { cout << head; if (sizeof...(tail)) { cout << ' '; } print(forward(tail)...); } template inline ostream& operator<<(ostream &strm, const vector &vec) { static constexpr const char *delim[] = {" ", ""}; for (const auto &e: vec) { strm << e << delim[&e == &vec.back()]; } return strm; } template inline vector make_v(const T &initValue, size_t sz) { return vector(sz, initValue); } template inline auto make_v(const T &initValue, size_t sz, Args... args) { return vector(initValue, args...))>(sz, make_v(initValue, args...)); } template class FixPoint : Func { public: explicit constexpr FixPoint(Func&& f) noexcept : Func(forward(f)) {} template constexpr decltype(auto) operator()(Args&&... args) const { return Func::operator()(*this, std::forward(args)...); } }; template static inline constexpr decltype(auto) makeFixPoint(Func&& f) noexcept { return FixPoint{forward(f)}; } template inline bool chmax(T &a, const T &b) noexcept { return b > a && (a = b, true); } template inline bool chmin(T &a, const T &b) noexcept { return b < a && (a = b, true); } template inline T diff(const T &a, const T &b) noexcept { return a < b ? b - a : a - b; } // }}} constexpr intmax_t MOD = intmax_t(1e9) + 7; // Mint {{{ template class ModInt { intmax_t value; public: inline ModInt(const ModInt& other) noexcept : value(other.value) {} inline ModInt(intmax_t value = 0) noexcept : value((value >= MOD) ? value % MOD : (value < 0) ? (value + MOD) % MOD : value) {} inline ModInt inv() const noexcept { return pow(value, MOD - 2); } inline ModInt& operator+=(const ModInt& other) noexcept { value = (value + other.value) % MOD; return *this; } inline ModInt& operator-=(const ModInt& other) noexcept { value = (MOD + value - other.value) % MOD; return *this; } inline ModInt& operator*=(const ModInt& other) noexcept { value = (value * other.value) % MOD; return *this; } inline ModInt& operator/=(const ModInt& other) noexcept { value = (value * other.inv().value) % MOD; return *this; } inline ModInt operator+(const ModInt& other) noexcept { return ModInt(*this) += other; } inline ModInt operator-(const ModInt& other) noexcept { return ModInt(*this) -= other; } inline ModInt operator*(const ModInt& other) noexcept { return ModInt(*this) *= other; } inline ModInt operator/(const ModInt& other) noexcept { return ModInt(*this) /= other; } inline bool operator==(const ModInt& other) noexcept { return value == *other; } inline bool operator!=(const ModInt& other) noexcept { return value != *other; } template explicit inline operator int_() const noexcept { return static_cast(value); } friend ostream& operator<<(ostream &os, ModInt other) noexcept { os << other.value; return os; } friend istream& operator>>(istream &is, ModInt& other) noexcept { is >> other.value; return is; } static constexpr inline ModInt pow(intmax_t n, intmax_t p) noexcept { intmax_t ret = 1; for (; p > 0; p >>= 1) { if (p & 1) ret = (ret * n) % MOD; n = (n * n) % MOD; } return ret; } }; using Mint = ModInt; // }}} signed main() { ios_base::sync_with_stdio(false); cin.tie(nullptr); var(size_t, N); var(Mint, p); if (N == 1) { return print(0), 0; } else if (N == 2) { return print(1), 0; } vector a(N + 1); a[1] = 0; a[2] = 1; reps(i, 3, N) { a[i] = p * a[i - 1] + a[i - 2]; } Mint res = 0, cumSum = 0; reps(i, 1, N) { cumSum += a[i]; res += a[i] * cumSum; } print(res); return 0; }