#define _USE_MATH_DEFINES #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 unless(c) if (!(c)) #define sz(x) ((int)(x).size()) #define all(x) (x).begin(),(x).end() #define rall(x) (x).rbegin(),(x).rend() #define range_it(a, l, r) (a).begin() + (l), (a).begin() + (r) 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 PQ = priority_queue; templateusing PQS = priority_queue, greater>; constexpr int inf = (int)1e9; constexpr ll inf_ll = (ll)1e18, MOD = 1000000007; constexpr LD PI = M_PI, EPS = 1e-12; // --- input --- // #ifdef _WIN32 #define getchar_unlocked _getchar_nolock #define putchar_unlocked _putchar_nolock #define fwrite_unlocked fwrite #define fflush_unlocked fflush #endif class Input { static int gc() { return getchar_unlocked(); } templatestatic void i(T& v) { cin >> v; } static void i(char& v) { while (isspace(v = gc())); } static void i(bool& v) { v = in() != '0'; } static void i(string& v) { v.clear(); char c; for (i(c); !isspace(c); c = gc())v += c; } static void i(int& v) { bool neg = false; v = 0; char c; i(c); if (c == '-') { neg = true; c = gc(); } for (; isdigit(c); c = gc())v = v * 10 + (c - '0'); if (neg)v = -v; } static void i(long long& v) { bool neg = false; v = 0; char c; i(c); if (c == '-') { neg = true; c = gc(); } for (; isdigit(c); c = gc())v = v * 10 + (c - '0'); if (neg)v = -v; } static void i(double& v) { double dp = 1; bool neg = false, adp = false; v = 0; char c; i(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; } static void i(long double& v) { long double dp = 1; bool neg = false, adp = false; v = 0; char c; i(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; } templatestatic void i(pair& v) { i(v.first); i(v.second); } templatestatic void i(vector& v) { for (auto& e : v)i(e); } templatestatic void input_tuple(T& v) { if constexpr (N < tuple_size_v) { i(get(v)); input_tuple(v); } } templatestatic void i(tuple& v) { InputTuple(v); } struct InputV { int n, m; InputV(int _n) :n(_n), m(0) {} InputV(const pair& nm) :n(nm.first), m(nm.second) {} templateoperator vector() { vector v(n); i(v); return v; } templateoperator vector>() { vector> v(n, vector(m)); i(v); return v; } }; public: static string get_line() { string v; char c; for (i(c); c != '\n' && c != '\0'; c = gc())v += c; return v; } templatestatic T in() { T v; i(v); return v; } templateoperator T()const { return in(); } int operator--(int)const { return in() - 1; } InputV operator[](int n)const { return InputV(n); } InputV operator[](const pair& n)const { return InputV(n); } void operator()()const {} templatevoid operator()(H&& h, T&& ...t)const { i(h); operator()(forward(t)...); } private: templateclass, class...>struct Multiple; templateclass V, class Head, class... Tail>struct Multiple { templateusing vec = V, Args...>; using type = typename Multiple::type; }; templateclass V>struct Multiple { using type = V<>; }; templateusing multiple_t = typename Multiple::type; templatevoid in_multiple(T& t)const { if constexpr (N < tuple_size_v) { auto& vec = get(t); using V = typename remove_reference_t::value_type; vec.push_back(in()); in_multiple(t); } } public: templateauto multiple(int h)const { multiple_t res; while (h--)in_multiple(res); return res; } #define input(T) Input::in() #define INT input(int) #define LL input(ll) #define STR input(string) #define inputs(T, ...) T __VA_ARGS__; in(__VA_ARGS__) #define ini(...) inputs(int, __VA_ARGS__) #define inl(...) inputs(ll, __VA_ARGS__) #define ins(...) inputs(string, __VA_ARGS__) }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 }; void p(int v)const { if (v < 0)putchar_unlocked('-'), v = -v; char b[10]; int i = 0; while (v)b[i++] = '0' + v % 10, v /= 10; if (!i)b[i++] = '0'; while (i--)putchar_unlocked(b[i]); } void p(ll v)const { if (v < 0)putchar_unlocked('-'), v = -v; char b[20]; int i = 0; while (v)b[i++] = '0' + v % 10, v /= 10; if (!i)b[i++] = '0'; while (i--)putchar_unlocked(b[i]); } void p(bool v)const { p(v ? B.t : B.f); } void p(char v)const { putchar_unlocked(v); } void p(const char* v)const { fwrite_unlocked(v, 1, strlen(v), stdout); } void p(double v)const { printf("%.20f", v); } void p(long double v)const { printf("%.20Lf", v); } template void p(const T& v)const { cout << v; } templatevoid p(const pair& v)const { p(v.first); p(D.d); p(v.second); } templatevoid p(const vector& v)const { rep(i, sz(v)) { if (i)p(D.d); p(v[i]); } } templatevoid p(const vector>& v)const { rep(i, sz(v)) { if (i)p(D.l); p(v[i]); } } public: Output& operator()() { p(D.l); return *this; } templateOutput& operator()(H&& h) { p(h); p(D.l); return *this; } templateOutput& operator()(H&& h, T&& ...t) { p(h); p(D.d); return operator()(forward(t)...); } templateOutput& range(const It& l, const It& r) { for (It i = l; i != r; i++) { if (i != l)p(D.d); p(*i); } p(D.l); return *this; } templateOutput& range(const T& a) { range(a.begin(), a.end()); return *this; } templatevoid exit(T&& ...t) { operator()(forward(t)...); std::exit(EXIT_SUCCESS); } Output& flush() { fflush_unlocked(stdout); return *this; } Output& set(const BoolStr& b) { B = b; return *this; } Output& set(const DivStr& d) { D = d; return *this; } Output& set(const char* t, const char* f) { B = BoolStr(t, f); return *this; } }out; // --- step --- // templatestruct Step { class It { T a, b, c; public: constexpr It() : a(T()), b(T()), c(T()) {} constexpr It(T _b, T _c, T _s) : a(_b), b(_c), c(_s) {} constexpr It& operator++() { --b; a += c; return *this; } constexpr It operator++(int) { It tmp = *this; --b; a += c; return tmp; } constexpr const T& operator*()const { return a; } constexpr const T* operator->()const { return &a; } constexpr bool operator==(const It& i)const { return b == i.b; } constexpr bool operator!=(const It& i)const { return !(b == i.b); } constexpr T start()const { return a; } constexpr T count()const { return b; } constexpr T step()const { return c; } }; constexpr Step(T b, T c, T s) : be(b, c, s) {} constexpr It begin()const { return be; } constexpr It end()const { return en; } constexpr T start()const { return be.start(); } constexpr T count()const { return be.count(); } constexpr T step()const { return be.step(); } constexpr T sum()const { return start() * count() + step() * (count() * (count() - 1) / 2); } operator vector()const { return as_vector(); } templatevoid each(const F& f)const { for (T i : *this)f(i); } auto as_vector()const { vector res; res.reserve(count()); each([&](T i) {res.push_back(i); }); return res; } template>auto map(const F& f)const { vector res; res.reserve(count()); each([&](T i) {res.push_back(f(i)); }); return res; } templateauto select(const F& f)const { vector res; each([&](T i) {if (f(i))res.push_back(i); }); return res; } templateint count_if(const F& f)const { int res = 0; each([&](T i) {if (f(i))++res; }); return res; } templateoptional find_if(const F& f)const { for (T i : *this)if (f(i))return i; return nullopt; } templateauto max_by(const F& f)const { auto v = map(f); return *max_element(v.begin(), v.end()); } templateauto min_by(const F& f)const { auto v = map(f); return *min_element(v.begin(), v.end()); } templatebool all_of(const F& f)const { for (T i : *this)if (!f(i))return false; return true; } templatebool any_of(const F& f)const { for (T i : *this)if (f(i))return true; return false; } template>auto sum(const F& f)const { U res = 0; each([&](T i) {res += static_cast(f(i)); }); return res; } using value_type = T; using iterator = It; private: It be, en; }; templateinline constexpr auto step(T a) { return Step(0, a, 1); } templateinline constexpr auto step(T a, T b) { return Step(a, b - a, 1); } templateinline constexpr auto step(T a, T b, T c) { return Step(a, a < b ? (b - a - 1) / c + 1 : 0, c); } // --- functions --- // inline namespace { templateinline void Sort(T& a) { sort(all(a)); } templateinline void RSort(T& a) { sort(rall(a)); } templateinline void Sort(T& a, const F& f) { sort(all(a), f); } templateinline void RSort(T& a, const F& f) { sort(rall(a), f); } templateinline T Sorted(T a) { Sort(a); return a; } templateinline T RSorted(T a) { RSort(a); return a; } templateinline T Sorted(T& a, const F& f) { Sort(a, f); return a; } templateinline T RSorted(T& a, const F& f) { RSort(a, f); return a; } templateinline void SortBy(T& a, const F& f) { sort(all(a), [&](const auto& x, const auto& y) {return f(x) < f(y); }); } templateinline void RSortBy(T& a, const F& f) { sort(rall(a), [&](const auto& x, const auto& y) {return f(x) < f(y); }); } templateinline void Reverse(T& a) { reverse(all(a)); } templateinline void Unique(T& a) { a.erase(unique(all(a)), a.end()); } templateinline void Uniq(T& a) { Sort(a); Unique(a); } templateinline void Rotate(T& a, int left) { rotate(a.begin(), a.begin() + left, a.end()); } templateinline T Reversed(T a) { Reverse(a); return a; } templateinline T Uniqued(T a) { Unique(a); return a; } templateinline T Uniqed(T a) { Uniq(a); return a; } templateinline T Rotated(T a, int left) { Rotate(a, left); return a; } templateinline auto Max(const T& a) { return *max_element(all(a)); } templateinline auto Min(const T& a) { return *min_element(all(a)); } templateinline int MaxPos(const T& a) { return max_element(all(a)) - a.begin(); } templateinline int MinPos(const T& a) { return min_element(all(a)) - a.begin(); } templateinline auto MaxBy(const T& a, const F& f) { return *max_element(all(a), [&](const auto& x, const auto& y) {return f(x) < f(y); }); } templateinline auto MinBy(const T& a, const F& f) { return *min_element(all(a), [&](const auto& x, const auto& y) {return f(x) < f(y); }); } templateinline int Count(const T& a, const U& v) { return count(all(a), v); } templateinline int CountIf(const T& a, const F& f) { return count_if(all(a), f); } templateinline int Find(const T& a, const U& v) { return find(all(a), v) - a.begin(); } templateinline int FindIf(const T& a, const F& f) { return find_if(all(a), f) - a.begin(); } templateinline U Sum(const T& a) { return accumulate(all(a), U()); } templateinline bool Includes(const T& a, const U& v) { return find(all(a), v) != a.end(); } templateinline auto Sum(const T& v, const F& f) { return accumulate(next(v.begin()), v.end(), f(*v.begin()), [&](auto a, auto b) {return a + f(b); }); } templateinline int Lower(const T& a, const U& v) { return lower_bound(all(a), v) - a.begin(); } templateinline int Upper(const T& a, const U& v) { return upper_bound(all(a), v) - a.begin(); } templateinline void RemoveIf(T& a, const F& f) { a.erase(remove_if(all(a), f), a.end()); } templateinline auto Vector(size_t size, const F& f) { vector> res(size); for (size_t i = 0; i < size; ++i)res[i] = f(i); return res; } templateinline auto Grid(size_t h, size_t w, const T& v = T()) { return vector>(h, vector(w, v)); } templateinline auto Slice(const T& v, size_t i, size_t len) { return i < v.size() ? T(v.begin() + i, v.begin() + min(i + len, v.size())) : T(); } templateinline auto Each(T& v, F&& f) { for (auto& i : v)f(i); } templateinline auto Select(const T& v, const F& f) { T res; for (const auto& e : v)if (f(e))res.push_back(e); return res; } templateinline auto Map(const T& v, F&& f) { vector> res(v.size()); size_t i = 0; for (const auto& e : v)res[i++] = f(e); return res; } templateinline auto MapIndex(const T& v, const F& f) { vector> res(v.size()); size_t i = 0; for (auto it = v.begin(); it != v.end(); ++it, ++i)res[i] = f(i, *it); return res; } templateinline auto TrueIndex(const T& v, const F& f) { vector res; for (size_t i = 0; i < v.size(); ++i)if (f(v[i]))res.push_back(i); return res; } templateinline auto Indexed(const T& v) { vector> res(v.size()); for (int i = 0; i < (int)v.size(); ++i)res[i] = make_pair(static_cast(v[i]), i); return res; } inline auto operator*(string s, size_t n) { string res; for (size_t i = 0; i < n; ++i)res += s; return res; } templateinline auto& operator<<(vector& v, const vector& v2) { v.insert(v.end(), all(v2)); return v; } templateinline T Ceil(T n, T m) { return (n + m - 1) / m; } templateinline T Ceil2(T n, T m) { return Ceil(n, m) * m; } templateinline T Tri(T n) { return (n & 1) ? (n + 1) / 2 * n : n / 2 * (n + 1); } templateinline T nC2(T n) { return (n & 1) ? (n - 1) / 2 * n : n / 2 * (n - 1); } templateinline T Mid(const T& l, const T& r) { return l + (r - l) / 2; } inline int pop_count(int n) { return bitset<32>(n).count(); } inline int pop_count(ll n) { return bitset<64>(n).count(); } templateinline bool chmax(T& a, const T& b) { if (a < b) { a = b; return true; } return false; } templateinline bool chmin(T& a, const T& b) { if (a > b) { a = b; return true; } return false; } templateinline bool inRange(const T& v, const T& min, const T& max) { return min <= v && v < max; } templateinline bool isSquere(T n) { T s = sqrt(n); return s * s == n || (s + 1) * (s + 1) == n; } templateinline T BIT(int b) { return T(1) << b; } templateinline U Gcdv(const T& v) { return accumulate(next(v.begin()), v.end(), U(*v.begin()), gcd); } templateinline U Lcmv(const T& v) { return accumulate(next(v.begin()), v.end(), U(*v.begin()), lcm); } templateinline T Pow(T a, T n) { 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) { T r = 1; while (n > 0) { if (n & 1)r = r * a % m, n--; else a = a * a % m, n /= 2; }return r; } } // --- 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) :n(x% MOD) { if (n < 0)n += MOD; } constexpr int get_mod()const { return MOD; } constexpr modint operator+()const { return *this; } constexpr modint operator-()const { return n ? MOD - n : 0; } constexpr modint& operator++() { if (MOD <= ++n)n = 0; return *this; } constexpr modint& operator--() { if (n <= 0)n = MOD; n--; return *this; } constexpr modint operator++(int) { modint t = *this; ++* this; return t; } constexpr modint operator--(int) { modint t = *this; --* this; return t; } constexpr modint next()const { return ++modint(*this); } constexpr modint pred()const { return --modint(*this); } constexpr modint operator+(const modint& m)const { return modint(*this) += m; } constexpr modint operator-(const modint& m)const { return modint(*this) -= m; } constexpr modint operator*(const modint& m)const { return modint(*this) *= m; } constexpr modint operator/(const modint& m)const { return modint(*this) /= m; } constexpr modint& operator+=(const modint& m) { n += m.n; if (n >= MOD)n -= MOD; return *this; } constexpr modint& operator-=(const modint& m) { n -= m.n; if (n < 0)n += MOD; return *this; } constexpr modint& operator*=(const modint& m) { n = n * m.n % MOD; return *this; } constexpr modint& operator/=(const modint& m) { 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 { return n == m.n; } constexpr bool operator!=(const modint& m)const { return n != m.n; } constexpr modint pow(T m)const { modint t = n, res = 1; while (m > 0) { if (m & 1)res *= t; t *= t; m >>= 1; } return res; } constexpr modint operator^(T m)const { return pow(m); } friend ostream& operator<<(ostream& os, const modint& m) { return os << m.n; } friend istream& operator>>(istream& is, modint& m) { return is >> m.n; } }; using mint = modint<1000000007>; using VM = vector; inline mint operator""_m(unsigned long long n) { return n; } int main() { int n = in, q = in; VL a = in[n]; VM dp(n + 1); dp[0] = a[0] - 1; dp[1] = 1; FOR(i, 1, n) { VM dp2(n + 1); rep(j, n)if (dp[j] != 0) { dp2[j] += dp[j] * (a[i] - 1); dp2[j + 1] += dp[j]; } dp = dp2; } rep(i, q) { out(dp[INT]); } }