#include using namespace std; #define rep(i,n) for(long long i = 0; i < (long long)(n); i++) #define repi(i,a,b) for(long long i = (long long)(a); i < (long long)(b); i++) using ll = long long; using vll = vector; using vvll = vector; static const long long mo = 1e9+7; template ostream &operator<<(ostream &o, const pair &v) { o << "(" << v.first << ", " << v.second << ")"; return o; } template struct seq{}; template struct gen_seq : gen_seq{}; template struct gen_seq<0, Is...> : seq{}; template void print_tuple(basic_ostream& os, Tuple const& t, seq){ using s = int[]; (void)s{0, (void(os << (Is == 0? "" : ", ") << get(t)), 0)...}; } template auto operator<<(basic_ostream& os, tuple const& t) -> basic_ostream& { os << "("; print_tuple(os, t, gen_seq()); return os << ")"; } ostream &operator<<(ostream &o, const vvll &v) { rep(i, v.size()) { rep(j, v[i].size()) o << v[i][j] << " "; cout << endl; } return o; } template ostream &operator<<(ostream &o, const vector &v) { o << '['; rep(i, v.size()) o << v[i] << (i != v.size()-1 ? ", " : ""); o << "]"; return o; } template ostream &operator<<(ostream &o, const set &m) { o << '['; for (auto it = m.begin(); it != m.end(); it++) o << *it << (next(it) != m.end() ? ", " : ""); o << "]"; return o; } template ostream &operator<<(ostream &o, const map &m) { o << '['; for (auto it = m.begin(); it != m.end(); it++) o << *it << (next(it) != m.end() ? ", " : ""); o << "]"; return o; } template ostream &operator<<(ostream &o, const unordered_map &m) { o << '['; for (auto it = m.begin(); it != m.end(); it++) o << *it; o << "]"; return o; } void printbits(ll mask, ll n) { rep(i, n) { cout << !!(mask & (1ll << i)); } cout << endl; } #define ldout fixed << setprecision(40) class Mod { public: int num; int mod; Mod() : Mod(0) {} Mod(long long int n) : Mod(n, 1000000007) {} Mod(long long int n, int m) { mod = m; num = (n % mod + mod) % mod;} Mod(const string &s){ long long int tmp = 0; for(auto &c:s) tmp = (c-'0'+tmp*10) % mod; num = tmp; } Mod(int n) : Mod(static_cast(n)) {} operator int() { return num; } void setmod(const int mod) { this->mod = mod; } }; istream &operator>>(istream &is, Mod &x) { long long int n; is >> n; x = n; return is; } ostream &operator<<(ostream &o, const Mod &x) { o << x.num; return o; } Mod operator+(const Mod a, const Mod b) { return Mod((a.num + b.num) % a.mod); } Mod operator+(const long long int a, const Mod b) { return Mod(a) + b; } Mod operator+(const Mod a, const long long int b) { return b + a; } Mod operator++(Mod &a) { return a + Mod(1); } Mod operator-(const Mod a, const Mod b) { return Mod((a.mod + a.num - b.num) % a.mod); } Mod operator-(const long long int a, const Mod b) { return Mod(a) - b; } Mod operator--(Mod &a) { return a - Mod(1); } Mod operator*(const Mod a, const Mod b) { return Mod(((long long)a.num * b.num) % a.mod); } Mod operator*(const long long int a, const Mod b) { return Mod(a)*b; } Mod operator*(const Mod a, const long long int b) { return Mod(b)*a; } Mod operator*(const Mod a, const int b) { return Mod(b)*a; } Mod operator+=(Mod &a, const Mod b) { return a = a + b; } Mod operator+=(long long int &a, const Mod b) { return a = a + b; } Mod operator-=(Mod &a, const Mod b) { return a = a - b; } Mod operator-=(long long int &a, const Mod b) { return a = a - b; } Mod operator*=(Mod &a, const Mod b) { return a = a * b; } Mod operator*=(long long int &a, const Mod b) { return a = a * b; } Mod operator*=(Mod& a, const long long int &b) { return a = a * b; } Mod factorial(const long long n) { if (n < 0) return 0; Mod ret = 1; for (int i = 1; i <= n; i++) { ret *= i; } return ret; } Mod operator^(const Mod a, const long long n) { if (n == 0) return Mod(1); Mod res = (a * a) ^ (n / 2); if (n % 2) res = res * a; return res; } Mod modpowsum(const Mod a, const long long b) { if (b == 0) return 0; if (b % 2 == 1) return modpowsum(a, b - 1) * a + Mod(1); Mod result = modpowsum(a, b / 2); return result * (a ^ (b / 2)) + result; } /*************************************/ // 以下、modは素数でなくてはならない! /*************************************/ Mod inv(const Mod a) { return a ^ (a.mod - 2); } Mod operator/(const Mod a, const Mod b) { assert(b.num != 0); return a * inv(b); } Mod operator/(const long long int a, const Mod b) { assert(b.num != 0); return Mod(a) * inv(b); } Mod operator/=(Mod &a, const Mod b) { assert(b.num != 0); return a = a * inv(b); } // n!と1/n!のテーブルを作る。 // nCrを高速に計算するためのもの。 // // assertでnを超えていないかをきちんとテストすること。 // // O(n log mo) vector fact, rfact; void constructFactorial(const long long n) { fact.resize(n); rfact.resize(n); fact[0] = rfact[0] = 1; for (int i = 1; i < n; i++) { fact[i] = fact[i-1] * i; rfact[i] = Mod(1) / fact[i]; } } // O(1) Mod nCr(const long long n, const long long r) { // assert(n < (long long)fact.size()); if (n < 0 || r < 0) return 0; return fact[n] * rfact[r] * rfact[n-r]; } // O(k log mo) Mod nCrWithoutConstruction(const long long n, const long long k) { if (n < 0) return 0; if (k < 0) return 0; Mod ret = 1; for (int i = 0; i < k; i++) { ret *= n - (Mod)i; ret /= Mod(i+1); } return ret; } // n*mの盤面を左下から右上に行く場合の数 // O(1) Mod nBm(const long long n, const long long m) { if (n < 0 || m < 0) return 0; return nCr(n + m, n); } /*************************************/ // 謎演算 /*************************************/ // gcdは関数__gcdを使いましょう。long long対応している。 // a x + b y = gcd(a, b) long long extgcd(long long a, long long b, long long &x, long long &y) { long long g = a; x = 1; y = 0; if (b != 0) g = extgcd(b, a % b, y, x), y -= (a / b) * x; return g; } /*************************************/ // GF(p)の行列演算 /*************************************/ using number = Mod; using arr = vector; using matrix = vector>; ostream &operator<<(ostream &o, const arr &v) { rep(i, v.size()) cout << v[i] << " "; cout << endl; return o; } ostream &operator<<(ostream &o, const matrix &v) { rep(i, v.size()) cout << v[i]; return o; } matrix zero(int n) { return matrix(n, arr(n, 0)); } // O(n^2) matrix identity(int n) { matrix A(n, arr(n, 0)); rep(i, n) A[i][i] = 1; return A; } // O(n^2) // O(n^2) arr mul(const matrix &A, const arr &x) { arr y(A.size(), 0); rep(i, A.size()) rep(j, A[0].size()) y[i] += A[i][j] * x[j]; return y; } // O(n^3) matrix mul(const matrix &A, const matrix &B) { matrix C(A.size(), arr(B[0].size(), 0)); rep(i, C.size()) rep(j, C[i].size()) rep(k, A[i].size()) C[i][j] += A[i][k] * B[k][j]; return C; } // 構築付なし累乗 // // O(n^3 log e) matrix pow(const matrix &A, long long e) { return e == 0 ? identity(A.size()) : e % 2 == 0 ? pow(mul(A, A), e/2) : mul(A, pow(A, e-1)); } // 構築付き累乗 // // powA: A^2^i // O(n^3 log e) matrix pow(const vector& powA, long long e) { // powA[0]がA // cout << powA[0] << "^" << e <& powA, long long e, arr& a) { // powA[0]がA // cout << powA[0] << "^" << e <& powA) { powA.clear(); powA.push_back(A); for (int i = 1; (1ll << i) < e; i++) { powA.push_back(mul(powA[i-1], powA[i-1])); } } int main(void) { ll n, c; cin >> n >> c; vll a(n); rep(i, a.size()) cin >> a[i]; matrix A = zero(n); rep(i, n) repi(j, i, n) A[j][i] = a[i]; vector powA; construct_powA(A, c+10, powA); arr x(n); rep(i, n) x[i] = 1; arr retvec = powmul(powA, c, x); Mod ret = retvec[n-1]; rep(i, n) ret -= (Mod(a[i]) ^ c); cout << ret << endl; return 0; }