#include using namespace std; #define REP(i,n) for(int i=0;i<(int)(n);++i) #define REPR(i,n) for (int i=(int)(n)-1;i>=0;--i) #define FOR(i,c) for(__typeof((c).begin())i=(c).begin();i!=(c).end();++i) #define ALL(c) (c).begin(), (c).end() #define valid(y,x,h,w) (0<=y&&y pii; templatebool chmax(T &a, const T &b) { if (abool chmin(T &a, const T &b) { if (bbasic_ostream& operator<<(basic_ostream&os, const C& c){os<<'[';for(auto i=begin(c);i!=end(c);++i)os<<(i==begin(c)?"":" ")<<*i;return os<<']';} templateostream&operator<<(ostream &o,const pair&t){return o<<'('<void output(ostream&,const Tp&){} templatevoid output(ostream &o,const Tp&t){if(N)o<<',';o<(t);output(o,t);} templateostream&operator<<(ostream&o,const tuple&t){o<<'(';output<0,tuple,Ts...>(o,t);return o<<')';} templatevoid output(T t,char z=10){if(t<0)t=-t,putchar(45);int c[20]; int k=0;while(t)c[k++]=t%10,t/=10;for(k||(c[k++]=0);k;)putchar(c[--k]^48);putchar(z);} templatevoid outputs(T t){output(t);} templatevoid outputs(S a,T...t){output(a,32);outputs(t...);} templatevoid output(T *a,int n){REP(i,n)cout<void output(T *a,int n,int m){REP(i,n)output(a[i],m);} templatebool input(T &t){int n=1,c;for(t=0;!isdigit(c=getchar())&&~c&&c-45;); if(!~c)return 0;for(c-45&&(n=0,t=c^48);isdigit(c=getchar());)t=10*t+c-48;t=n?-t:t;return 1;} templatebool input(S&a,T&...t){input(a);return input(t...);} templatebool inputs(T *a, int n) { REP(i,n) if(!input(a[i])) return 0; return 1;} template struct ModInt { int x; ModInt() : x(0) {} ModInt(ll s) { if ((x = s % MOD) < 0) x += MOD; } ModInt operator+=(ModInt rhs) { if ((x+=rhs.x) >= MOD) x -= MOD; return *this; } ModInt operator-=(ModInt rhs) { if ((x-=rhs.x) < 0) x += MOD; return *this; } ModInt operator*=(ModInt rhs) { x = (ll)x*rhs.x % MOD; return *this; } ModInt operator+(ModInt rhs) const { return ModInt(*this) += rhs; } ModInt operator-(ModInt rhs) const { return ModInt(*this) -= rhs; } ModInt operator*(ModInt rhs) const { return ModInt(*this) *= rhs; } ModInt operator/=(ModInt rhs) { static const ll inv2 = ModInt(2).inv().x; // 2で割るのは特別に保存してみる ll i = (rhs.x == 2 ? inv2 : rhs.inv().x); x = x*i%MOD; return *this; } ModInt operator/(ModInt rhs) const { return ModInt(*this) /= rhs; } ModInt inv() { return pow(MOD-2); } ModInt pow(ll n) const { ModInt r = 1, t = x; for (;n;n>>=1,t*=t) if (n&1) r *= t; return r; } static ModInt strnum(const string &n) {ModInt a = 0; for (char c:n) a = a*10+c-'0'; return a;} friend ostream& operator<<(ostream &os, const ModInt rhs){ return os << rhs.x; } }; typedef ModInt mint; template struct Matrix { T v[H][W]; int h,w; T* operator[](int i) { return v[i]; } const T* operator[](int i) const { return v[i]; } Matrix() : h(0),w(0) {} Matrix(int h, int w) : h(h),w(w) { REP(i,h)REP(j,w)v[i][j] = 0; } Matrix(const vector > &u) : h(u.size()),w(u[0].size()) { REP(i,h)REP(j,w)v[i][j]=u[i][j]; } static Matrix identity(int n) { Matrix A(n,n); REP(i,n) A[i][i] = 1; return A; } Matrix operator*(const Matrix &B) const { Matrix res(h,B.w); REP(i,h)REP(j,B.w) REP(k,w) res[i][j] += v[i][k] * B[k][j]; return res; } Matrix& operator*=(const Matrix &B) { return *this = *this * B; } Matrix& operator+=(const Matrix &B) { REP(i,h)REP(j,w)v[i][j]+=B[i][j]; return *this; } Matrix& operator-=(const Matrix &B) { REP(i,h)REP(j,w)v[i][j]-=B[i][j]; return *this; } Matrix operator+(const Matrix &B) const { return Matrix(*this)+=B; } Matrix operator-(const Matrix &B) const { return Matrix(*this)-=B; } Matrix pow(ll n) { Matrix A(*this); Matrix B = identity(h); for (;n;n>>=1) { if (n&1) B *= A; A *= A; } return B; } // vector vector operator*(const vector &b) const { vector res(w); REP(i,h) REP(j,w) res[i] += v[i][j] * b[j]; return res; } friend ostream &operator<<(ostream &os, const Matrix &rhs) { REP(i,rhs.h) REP(j,rhs.w) os << rhs[i][j] << (j!=rhs.w-1?' ':'\n'); return os; } }; typedef Matrix mat; int A[100000]; mint F[1000001]; void solve1(int n, int K) { mint sum = 0; REP(i,n) { F[i] = A[i]; sum += F[i]; } mint S = sum; for (int i=n; i v(n+1); REP(i,n) v[i] = A[n-1-i]; v[n] = A[0]; REP(i,n) M[0][i] = 1; REP(i,n-1) M[1+i][i] = 1; M[n][n] = 1; M[n][n-2] = 1; // cout << M << endl; vector t = M.pow(K-1) * v; // cout << t << endl; cout << t[n-1] << " " << t[n] << endl; } int main() { ll n,k; while(input(n,k)) { REP(i,n) input(A[i]); if (k<=1000000) { solve1(n,k); } else { solve2(n,k); } } }