#define _CRT_SECURE_NO_WARNINGS #include "bits/stdc++.h" #define rep(i, n) for(int i=0; i<(n); ++i) #define FOR(i, m, n) for(int i=(m); i<(n); ++i) #define rrep(i, n) for(int i=(n)-1; i>=0; --i) #define rfor(i, m, n) for(int i=(m); i>=(n); --i) #define sz(x) ((int)(x).size()) #define all(x) (x).begin(),(x).end() #define rall(x) (x).rbegin(),(x).rend() #define mp make_pair #define pb push_back #define eb emplace_back using namespace std; using LL = long long; using ld = long double; using VB = vector; using VVB = vector; using VI = vector; using VVI = vector; using VL = vector; using VVL = vector; using VS = vector; using VD = vector; using PII = pair; using VP = vector; using PLL = pair; using VPL = vector; templateusing Grid = vector>; templateusing PQ = priority_queue; templateusing PQS = priority_queue, greater>; constexpr int inf = (int)1e9; constexpr LL inf_ll = (LL)1e18, MOD = 1000000007; const ld PI = acosl(-1.0), EPS = 1e-12; templateinline void Sort(T& a)noexcept { sort(all(a)); } templateinline void RSort(T& a)noexcept { sort(rall(a)); } templateinline void Reverse(T& a)noexcept { reverse(all(a)); } templateinline void Unique(T& a)noexcept { a.erase(unique(all(a)), a.end()); } templateinline T Sorted(T a)noexcept { Sort(a); return a; } templateinline T RSorted(T a)noexcept { RSort(a); return a; } templateinline T Reversed(T a)noexcept { Reverse(a); return a; } templateinline T Uniqued(T a)noexcept { Unique(a); return a; } templateinline auto Max(const T& a)noexcept { return *max_element(all(a)); } templateinline auto Min(const T& a)noexcept { return *min_element(all(a)); } templateinline int MaxPos(const T& a)noexcept { return max_element(all(a)) - a.begin(); } templateinline int MinPos(const T& a)noexcept { return min_element(all(a)) - a.begin(); } templateinline int Count(const T& a, const U& v)noexcept { return count(all(a), v); } templateinline int Find(const T& a, const U& v)noexcept { auto pos = find(all(a), v); return pos == a.end() ? -1 : pos - a.begin(); } templateinline U Sum(const T& a, const U& v)noexcept { return accumulate(all(a), v); } templateinline int Lower(const T& a, const U& v)noexcept { return lower_bound(all(a), v) - a.begin(); } templateinline int Upper(const T& a, const U& v)noexcept { return upper_bound(all(a), v) - a.begin(); } templateinline void RemoveIf(T& a, P f)noexcept { a.erase(remove_if(all(a), f), a.end()); } templateinline T Age(T n, T m)noexcept { return (n + m - 1) / m; } templateinline T Age2(T n, T m)noexcept { return Age(n, m) * m; } templateinline T Tri(T n)noexcept { return (n & 1) ? (n + 1) / 2 * n : n / 2 * (n + 1); } templateinline T BIT(int b)noexcept { return T{ 1 } << b; } templateinline T Gcd(T n, T m)noexcept { return m ? Gcd(m, n % m) : n; } templateinline T Lcm(T n, T m)noexcept { return n / Gcd(n, m) * m; } templateinline T Pow(T a, T n)noexcept { T r = 1; while (n > 0) { if (n & 1)r *= a; a *= a; n /= 2; }return r; } templateinline T Powmod(T a, T n, T m = MOD)noexcept { T r = 1; while (n > 0) { if (n & 1)r = r * a % m, n--; else a = a * a % m, n /= 2; }return r; } templateinline bool chmax(T& a, const T& b)noexcept { if (a < b) { a = b; return true; } return false; } templateinline bool chmin(T& a, const T& b)noexcept { if (a > b) { a = b; return true; } return false; } templateinline bool inRange(const T& v, const T& min, const T& max)noexcept { return min <= v && v <= max; } inline string operator*(string s, int n)noexcept { string ret; rep(i, n)ret += s; return ret; } // --- input --- // #if defined(_WIN32) || defined(ONLINE_JUDGE) #define getchar_unlocked _getchar_nolock #define putchar_unlocked _putchar_nolock #endif inline int gc()noexcept { return getchar_unlocked(); } templateinline void InputF(T& v)noexcept { cin >> v; } inline void InputF(char& v)noexcept { while (isspace(v = gc())); } inline void InputF(string& v)noexcept { char c; for (InputF(c); !isspace(c); c = gc())v += c; } inline void InputF(int& v)noexcept { bool neg = false; v = 0; char c; InputF(c); if (c == '-') { neg = true; c = gc(); } for (; isdigit(c); c = gc())v = v * 10 + (c - '0'); if (neg)v = -v; } inline void InputF(long long& v)noexcept { bool neg = false; v = 0; char c; InputF(c); if (c == '-') { neg = true; c = gc(); } for (; isdigit(c); c = gc())v = v * 10 + (LL)(c - '0'); if (neg)v = -v; } inline void InputF(double& v)noexcept { double dp = 1; bool neg = false, adp = false; v = 0; char c; InputF(c); if (c == '-') { neg = true; c = gc(); } for (; isdigit(c) || c == '.'; c = gc()) { if (c == '.')adp = true; else if (adp)v += (c - '0') * (dp *= 0.1); else v = v * 10 + (c - '0'); } if (neg)v = -v; } templateinline void InputF(pair& v)noexcept { InputF(v.first); InputF(v.second); } templateinline void InputF(vector& v)noexcept { for (auto& e : v)InputF(e); } templateinline T input() { T v; InputF(v); return v; } struct InputV { int n, m; InputV(int N) :n(N), m(0) {} InputV(pair N) :n(N.first), m(N.second) {} templateoperator vector()noexcept { vector v(n); InputF(v); return v; } templateoperator vector>()noexcept { vector> v(n, vector(m)); InputF(v); return v; } }; struct Input { templateoperator T()noexcept { return input(); } int operator--(int) { int v; InputF(v); v--; return v; } InputV operator[](int n)noexcept { return InputV(n); } InputV operator[](pair n)noexcept { return InputV(n); } void operator()() {} templatevoid operator()(H&& h, T&& ...t) { InputF(h); operator()(forward(t)...); } templatearray, W> get(int H) { array, W> ret; rep(i, H)rep(j, W) { T x = *this; ret[j].push_back(x); } return ret; } }in; // --- output --- // struct BoolStr { const char* t, * f; BoolStr(const char* _t, const char* _f) :t(_t), f(_f) {} }Yes("Yes", "No"), yes("yes", "no"), YES("YES", "NO"), Int("1", "0"); struct DivStr { const char* d, * l; DivStr(const char* _d, const char* _l) :d(_d), l(_l) {} }spc(" ", "\n"), no_spc("", "\n"), end_line("\n", "\n"), comma(",", "\n"), no_endl(" ", ""); class Output { BoolStr B{ Yes }; DivStr D{ spc }; bool isPrint = true; void p(double v) { printf("%.20f", v); } void p(long double v) { printf("%.20Lf", v); } void p(int v) { printf("%d", v); } void p(LL v) { printf("%lld", v); } void p(char v) { putchar(v); } void p(bool v) { printf("%s", v ? B.t : B.f); } templatevoid p(const T& v) { cout << v; } templatevoid p(const pair& v) { p(v.first); printf("%s", D.d); p(v.second); } templatevoid p(const vector& v) { rep(i, sz(v)) { if (i)printf("%s", D.d); p(v[i]); } } templatevoid p(const vector>& v) { rep(i, sz(v)) { if (i)printf("%s", D.l); p(v[i]); } } void p(const BoolStr& v) { B = v; isPrint = false; } void p(const DivStr& v) { D = v; isPrint = false; } public: void operator()() { printf("%s", D.l); } templatevoid operator()(H&& h) { p(h); if (isPrint)printf("%s", D.l); isPrint = true; B = Yes; D = spc; } templatevoid operator()(H&& h, T&& ...t) { p(h); if (isPrint)printf("%s", D.d); isPrint = true; operator()(forward(t)...); } templatevoid exit(T&& ...t) { operator()(forward(t)...); std::exit(EXIT_SUCCESS); } }out; // --- dump --- // #if __has_include("dump.hpp") #include "dump.hpp" #else #define dump(...) (void(0)) #endif // ---------------------------------------------------------------- // templatestruct modint { using T = long long; T n; constexpr modint(const T x = 0)noexcept :n(x% MOD) { if (n < 0)n += MOD; } constexpr int get_mod()const noexcept { return MOD; } constexpr modint operator+()const noexcept { return *this; } constexpr modint operator-()const noexcept { return n ? MOD - n : 0; } constexpr modint& operator++()noexcept { if (MOD <= ++n)n = 0; return *this; } constexpr modint& operator--()noexcept { if (n <= 0)n = MOD; n--; return *this; } constexpr modint& operator++(int)noexcept { modint t = *this; ++* this; return t; } constexpr modint& operator--(int)noexcept { modint t = *this; --* this; return t; } constexpr modint next()const noexcept { modint t = *this; ++t; return t; } constexpr modint pred()const noexcept { modint t = *this; --t; return t; } constexpr modint operator+(const modint& m)const noexcept { return modint(*this) += m; } constexpr modint operator-(const modint& m)const noexcept { return modint(*this) -= m; } constexpr modint operator*(const modint& m)const noexcept { return modint(*this) *= m; } constexpr modint operator/(const modint& m)const noexcept { return modint(*this) /= m; } constexpr modint& operator+=(const modint& m)noexcept { n += m.n; if (n >= MOD)n -= MOD; return *this; } constexpr modint& operator-=(const modint& m)noexcept { n -= m.n; if (n < 0)n += MOD; return *this; } constexpr modint& operator*=(const modint& m)noexcept { n = n * m.n % MOD; return *this; } constexpr modint& operator/=(const modint& m)noexcept { assert(m.n); T a = m.n, b = MOD, u = 1, v = 0; while (b) { T t = a / b; a -= t * b; swap(a, b); u -= t * v; swap(u, v); } n = n * u % MOD; if (n < 0)n += MOD; return *this; } constexpr bool operator==(const modint& m)const noexcept { return n == m.n; } constexpr bool operator!=(const modint& m)const noexcept { return n != m.n; } constexpr modint pow(modint m)const noexcept { modint t = n, res = 1; while (m.n > 0) { if (m.n & 1)res *= t; t *= t; m.n >>= 1; } return res; } constexpr modint operator^(modint m)const noexcept { return pow(m); } }; using mint = modint<1000000007>; using VM = vector; ostream& operator<<(ostream& os, const modint& m)noexcept { return os << m.n; } istream& operator>>(istream& is, modint& m)noexcept { return is >> m.n; } mint operator""_m(unsigned long long n) { return n; } templateclass CulSum { int n; vector s; public: static vector bulid(const vector& a) { int N = a.size(); vector ret(N + 1); for (int i = 0; i < N; ++i)ret[i + 1] = ret[i] + a[i]; return ret; } templatestatic vector bulid(const U& a, F f) { int N = a.size(); vector ret(N + 1); for (int i = 0; i < N; ++i)ret[i + 1] = ret[i] + static_cast(f(a[i])); return ret; } CulSum(const vector& a) :n(a.size()) { s = bulid(a); } templateCulSum(const U& a, F f) : n(a.size()) { s = bulid(a, f); } // [l, r) T operator()(int l, int r)const { l = min(max(l, 0), n); r = min(max(r, 0), n); return l > r ? 0 : s[r] - s[l]; } // [0, r) T operator()(int r)const { r = min(max(r, 0), n); return s[r]; } vector get_s()const { return s; } }; int main() { int n = in; mint p = in; VM a(n); a[0] = 0; a[1] = 1; FOR(i, 2, n) { a[i] = a[i - 1] * p + a[i - 2]; } CulSum s(a); mint ans; rep(i, n) { ans += a[i] * s(i + 1); } out(ans); }