#include #define LLI long long int #define FOR(v, a, b) for(LLI v = (a); v < (b); ++v) #define FORE(v, a, b) for(LLI v = (a); v <= (b); ++v) #define REP(v, n) FOR(v, 0, n) #define REPE(v, n) FORE(v, 0, n) #define REV(v, a, b) for(LLI v = (a); v >= (b); --v) #define ALL(x) (x).begin(), (x).end() #define RALL(x) (x).rbegin(), (x).rend() #define ITR(it, c) for(auto it = (c).begin(); it != (c).end(); ++it) #define RITR(it, c) for(auto it = (c).rbegin(); it != (c).rend(); ++it) #define EXIST(c,x) ((c).find(x) != (c).end()) #define fst first #define snd second #define popcount __builtin_popcount #define UNIQ(v) (v).erase(unique(ALL(v)), (v).end()) #define bit(i) (1LL<<(i)) #ifdef DEBUG #include #else #define dump(...) ((void)0) #endif #define gcd __gcd using namespace std; template constexpr T lcm(T m, T n){return m/gcd(m,n)*n;} template void join(ostream &ost, I s, I t, string d=" "){for(auto i=s; i!=t; ++i){if(i!=s)ost< istream& operator>>(istream &is, vector &v){for(auto &a : v) is >> a; return is;} template bool chmin(T &a, const U &b){return (a>b ? a=b, true : false);} template bool chmax(T &a, const U &b){return (a void fill_array(T (&a)[N], const U &v){fill((U*)a, (U*)(a+N), v);} struct Init{ Init(){ cin.tie(0); ios::sync_with_stdio(false); } }init; template class ModInt{ public: uint64_t val; ModInt(): val(0){} ModInt(int64_t n){ if(n >= M) val = n % M; else if(n < 0) val = n % M + M; else val = n; } inline constexpr ModInt operator+(const ModInt &a) const {return ModInt((val+a.val)%M);} inline constexpr ModInt operator-(const ModInt &a) const {return ModInt((val-a.val+M)%M);} inline constexpr ModInt operator*(const ModInt &a) const {return ModInt((val*a.val)%M);} inline constexpr ModInt operator/(const ModInt &a) const {return ModInt((val*a.inv().val)%M);} inline constexpr ModInt& operator=(const ModInt &a){val = a.val; return *this;} inline constexpr ModInt& operator+=(const ModInt &a){if((val += a.val) >= M) val -= M; return *this;} inline constexpr ModInt& operator-=(const ModInt &a){if(val < a.val) val += M; val -= a.val; return *this;} inline constexpr ModInt& operator*=(const ModInt &a){(val *= a.val) %= M; return *this;} inline constexpr ModInt& operator/=(const ModInt &a){(val *= a.inv().val) %= M; return *this;} inline constexpr bool operator==(const ModInt &a) const {return val==a.val;} inline constexpr bool operator!=(const ModInt &a) const {return val!=a.val;} inline constexpr static ModInt power(LLI n, LLI p){ ModInt ret = 1, e = n; for(; p; e *= e, p >>= 1) if(p&1) ret *= e; return ret; } inline constexpr ModInt power(LLI p) const{return power(val,p);} inline constexpr ModInt inv() const{ int64_t a = val, b = M, u = 1, v = 0; while(b){ int64_t t = a/b; a -= t*b; swap(a,b); u -= t*v; swap(u,v); } u %= M; if(u < 0) u += M; return u; } }; template ModInt operator-(const ModInt &a){return M-a.val;} template ModInt operator+(int64_t a, const ModInt &b){return ModInt(ModInt(a)+b.val);} template ModInt operator-(int64_t a, const ModInt &b){return ModInt(ModInt(a)-b.val);} template ModInt operator*(int64_t a, const ModInt &b){return ModInt(ModInt(a)*b.val);} template ModInt operator/(int64_t a, const ModInt &b){return ModInt(ModInt(a)/b.val);} template istream& operator>>(istream &is, ModInt &a){is >> a.val; return is;} template ostream& operator<<(ostream &os, const ModInt &a){ os << a.val; return os;} template struct SquareMatrix{ int N; vector> matrix; SquareMatrix(): N(0){} SquareMatrix(int N): N(N), matrix(N, vector(N)){} SquareMatrix(int N, const T &val): N(N), matrix(N, vector(N, val)){} SquareMatrix(const vector> &matrix): N(matrix.size()), matrix(matrix){} SquareMatrix(const SquareMatrix &) = default; SquareMatrix(SquareMatrix &&) = default; SquareMatrix(initializer_list> list): N(list.size()), matrix(N, vector(N)){ int i = 0; ITR(it1,list){ int j = 0; ITR(it2,*it1){ matrix[i][j] = *it2; ++j; } ++i; } } SquareMatrix& operator=(const SquareMatrix &val){ N = val.N; matrix = val.matrix; return *this; } bool operator==(const SquareMatrix &val) const { return matrix == val.matrix; } bool operator!=(const SquareMatrix &val) const { return !(*this == val); } SquareMatrix& operator+=(const SquareMatrix &val){ REP(i,N) REP(j,N) matrix[i][j] = matrix[i][j] + val[i][j]; return *this; } SquareMatrix& operator-=(const SquareMatrix &val){ REP(i,N) REP(j,N) matrix[i][j] = matrix[i][j] - val[i][j]; return *this; } SquareMatrix& operator*=(const SquareMatrix &val){ vector> temp(N, vector(N)); REP(i,N) REP(j,N) REP(k,N) temp[i][j] = temp[i][j] + matrix[i][k] * val[k][j]; swap(matrix, temp); return *this; } inline const vector& operator[](size_t i) const {return matrix[i];} inline vector& operator[](size_t i){return matrix[i];} inline int size() const {return N;} static SquareMatrix make_unit(int N){ SquareMatrix ret(N); REP(i,N) ret[i][i] = 1; return ret; } SquareMatrix transpose() const{ SquareMatrix ret(N); REP(i,N) REP(j,N) ret[i][j] = matrix[j][i]; return ret; } void show(int w = 10) const { #ifdef DEBUG REP(i,N){ cerr << (i==0 ? "⎛" : (i==N-1 ? "⎝" : "⎜")); REP(j,N) cerr << setw(w) << matrix[i][j] << " "; cerr << (i==0 ? "⎞" : (i==N-1 ? "⎠" : "⎟")); cerr << endl; } #endif } }; template SquareMatrix operator+(const SquareMatrix &a, const SquareMatrix &b){auto ret = a; ret += b; return ret;} template SquareMatrix operator-(const SquareMatrix &a, const SquareMatrix &b){auto ret = a; ret -= b; return ret;} template SquareMatrix operator*(const SquareMatrix &a, const SquareMatrix &b){auto ret = a; ret *= b; return ret;} template SquareMatrix power(SquareMatrix a, uint64_t p){ int N = a.size(); if(p == 0) return SquareMatrix::make_unit(N); if(p == 1) return a; SquareMatrix temp = power(a, p/2); auto ret = temp * temp; if(p%2) ret *= a; return ret; } template vector operator*(const SquareMatrix &a, const vector &b){ vector ret(a.size()); REP(i,a.size()){ REP(j,a.size()){ ret[i] += a[i][j] * b[j]; } } return ret; } template vector operator*(const vector &b, const SquareMatrix &a){ vector ret(a.size()); REP(i,a.size()){ REP(j,a.size()){ ret[j] += b[i] * a[i][j]; } } return ret; } template bool inverse_matrix(SquareMatrix m, SquareMatrix &ret){ int N = m.size(); ret = SquareMatrix::make_unit(N); REP(i,N){ int p = i; FOR(j,i,N){ if(m[i][j] != 0){ p = j; break; } } swap(m[i], m[p]); swap(ret[i], ret[p]); { T d = m[i][i]; if(d == 0) return false; REP(j,N){ m[i][j] /= d; ret[i][j] /= d; } } REP(j,N){ if(i==j) continue; T d = m[j][i] / m[i][i]; REP(k,N){ m[j][k] -= m[i][k] * d; ret[j][k] -= ret[i][k] * d; } } } return true; } const LLI mod = 1e9+7; using mint = ModInt; using M = SquareMatrix; pair solve1(int N, LLI K, vector a){ M m(N); REP(i,N) m[0][i] = 1; REP(i,N-1) m[i+1][i] = 1; auto m2 = power(m,K-N); reverse(ALL(a)); vector A(N); REP(i,N) A[i] = a[i]; auto b = m2 * A; mint f = b[0]; mint s = accumulate(ALL(a), 0); M c; auto t = M::make_unit(N)-m; inverse_matrix(t,c); auto temp = (M::make_unit(N)-power(m,K-N+1)) * c; temp -= M::make_unit(N); auto B = temp * A; s += B[0]; return {f,s}; } pair solve2(int N, LLI K, vector a){ vector v(K); mint temp = 0; REP(i,N){ temp += a[i]; v[i] = a[i]; } FOR(i,N,K){ v[i] = temp; temp += v[i]; temp -= v[i-N]; } mint f = v.back(); mint s = 0; for(auto &x : v) s += x; return {f,s}; } int main(){ LLI N,K; while(cin >> N >> K){ vector a(N); cin >> a; pair ans; if(K > 1000000) ans = solve1(N,K,a); else ans = solve2(N,K,a); cout << ans.fst << " " << ans.snd << endl; } return 0; }