//yukicoder@cpp17 #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include using namespace std; using ll = long long; using P = pair; const ll MOD = 998244353; const ll MODx = 1000000007; const int INF = (1<<30)-1; const ll LINF = (1LL<<62LL)-1; const double EPS = (1e-10); P ar4[4] = {{0,1},{0,-1},{1,0},{-1,0}}; P ar8[8] = {{-1,-1},{-1,0},{-1,1},{0,-1},{0,1},{1,-1},{1,0},{1,1}}; template vector make_vector(size_t a, T b) { return vector(a, b); } template auto make_vector(size_t a, Ts... ts) { return vector(a, make_vector(ts...)); } /* 確認ポイント cout << fixed << setprecision(n) << 小数計算//n桁の小数表記になる 計算量は変わらないが楽できるシリーズ min(max)_element(iter,iter)で一番小さい(大きい)値のポインタが帰ってくる count(iter,iter,int)でintがiterからiterの間にいくつあったかを取得できる */ /* function corner below */ /* Function corner above */ /* comment outed because can cause bugs __attribute__((constructor)) void initial() { cin.tie(0); ios::sync_with_stdio(false); } */ template struct ModInt{ int n; ModInt():n(0){} ModInt(long long n_):n(n_ >= 0 ? n_%mod : mod - ((-n_)%mod) ){} ModInt(int n_):n(n_ >= 0 ? n_%mod : mod - ((-n_)%mod) ){} ModInt &operator+=(const ModInt &p){ if((n+=p.n) >= mod)n-=mod; return *this; } ModInt &operator-=(const ModInt &p){ n+=mod-p.n; if(n >= mod)n-=mod; return *this; } ModInt &operator*=(const ModInt &p){ n = (int) ((1LL*n*p.n)%mod); return *this; } ModInt &operator/=(const ModInt &p){ *this *= p.inverse(); return *this; } ModInt operator-() const {return ModInt(-n);} ModInt operator+(const ModInt &p) const {return ModInt(*this) += p;} ModInt operator-(const ModInt &p) const {return ModInt(*this) -= p;} ModInt operator*(const ModInt &p) const {return ModInt(*this) *= p;} ModInt operator/(const ModInt &p) const {return ModInt(*this) /= p;} bool operator==(const ModInt &p) const {return n==p.n;} bool operator<(const ModInt &p) const {return n(const ModInt &p) const {return n>p.n;} bool operator>=(const ModInt &p) const {return n>=p.n;} bool operator<=(const ModInt &p) const {return n<=p.n;} bool operator!=(const ModInt &p) const {return n!=p.n;} ModInt inverse() const { int a = n,b = mod,u = 1,v = 0; while(b){ int t = a/b; a -= t*b; swap(a,b); u -= t*v; swap(u,v); } return ModInt(u); } ModInt pow(int64_t z) const { ModInt ret(1),mul(n); while(z > 0){ if(z & 1) ret *= mul; mul *= mul; z >>= 1; } return ret; } friend ostream &operator<<(ostream &os, const ModInt &p){ return os << p.n; } friend istream &operator>>(istream &is, ModInt &a){ int64_t t; is >> t; a = ModInt ((long long)t); return (is); } }; using mint = ModInt; template struct mat{ vector> x; int h,w; mat():x(vector>()){} mat(int h,int w):x(vector>(h,vector(w))),h(h),w(w){} mat(int h,int w, T c):x(vector>(h,vector(w,c))),h(h),w(w){} mat(vector> A):x(A),h(A.size()),w(A[0].size()){} vector& operator[](int i){return x[i];} void resize(int h, int w){ x.assign(h, vector(w, 0)); } mat base(){ return mat(h,w,0); } mat& operator*=(mat& y){ mat ret(h,y.w,0); if(w != y.h){ for(int i = 0; h > i; i++){ for(int j = 0; y.w > j; j++){ ret[i][j] = -1; } } }else{ for(int i = 0; h > i; i++){ for(int j = 0; y.w > j; j++){ for(int k = 0; w > k; k++){ ret[i][j] = ret[i][j] + x[i][k]*y[k][j]; } } } } for(int i = 0; h > i; i++){ x[i].resize(y.w); } w = y.w; for(int i = 0; h > i; i++){ for(int j = 0; y.w > j; j++){ x[i][j] = ret[i][j]; } } return *this; } mat operator*(mat& y){return mat(*this) *= y;} mat pow(long long n){//正方行列のみ mat res(h,w); mat ret(h,w,0); mat a(h,w); for(int i = 0; h > i; i++){ ret[i][i] = 1; } for(int i = 0; h > i; i++){ for(int j = 0; w > j; j++){ a[i][j] = (*this)[i][j]; } } while(n > 0){ if(n & 1){ ret *= a; } a *= a; n/=2; } for(int i = 0; h > i; i++){ for(int j = 0; w > j; j++){ res[i][j] = ret[i][j]; } } return res; } // Requirement: h==w pair inv(){ if(h != w)return {false, base()}; mat gaussianMat(h, 2*w, 0); for(int i = 0; h > i; i++){ for(int j = 0; w > j; j++){ gaussianMat[i][j] = (*this)[i][j]; } } for(int i = 0; h > i; i++){ gaussianMat[i][w+i] = 1; } for(int i = 0; h > i; i++){ for(int j = i; h > j; j++){ if(gaussianMat[j][i] != 0){ swap(gaussianMat[i], gaussianMat[j]); } } T initCoeffient = gaussianMat[i][i]; if(initCoeffient == 0){ return {false, base()}; } for(int j = 0; 2*w > j; j++){ gaussianMat[i][j] /= initCoeffient; } for(int j = i+1; h > j; j++){ T deleteCoeffient = gaussianMat[j][i] * -1; for(int k = i; 2*w > k; k++){ gaussianMat[j][k] += deleteCoeffient * gaussianMat[i][k]; } } } for(int i = 0; h > i; i++){ if(gaussianMat[i][i] != 1){ T normarizeCoeffient = gaussianMat[i][i]; if(normarizeCoeffient == 0)continue; for(int j = i; 2*w > j; j++){ gaussianMat[i][j] /= normarizeCoeffient; } } } for(int i = h-1; 0 <= i; i--){ for(int j = 0; i > j; j++){ T deleteCoeffient = gaussianMat[j][i] * -1; for(int k = i; 2*w > k; k++){ gaussianMat[j][k] += deleteCoeffient * gaussianMat[i][k]; } } } mat v(h, w); for(int i = 0; h > i; i++){ for(int j = 0; w > j; j++){ v[i][j] = gaussianMat[i][j+w]; } } return {true, v}; } friend istream &operator>>(istream &is, mat &m){ for(int i = 0; m.h > i; i++){ for(int j = 0; m.w > j; j++){ is>>m.x[i][j]; } } return is; } friend ostream &operator<<(ostream &os, const mat &m){ for(int i = 0; m.h > i; i++){ for(int j = 0; m.w > j; j++){ os << m.x[i][j]; if(j+1 != m.w)cout << " "; } if(i+1 != m.h)cout << "\n"; } return os; } }; void solve1(int n, long long k){ mat A(n+1,n+1,0); for(int i = 0; n > i; i++){ A[0][i] = 1; } for(int i = 0; n-1 > i; i++){ A[i+1][i] = 1; } A[n][0] = A[n][n] = 1; mat B(n+1,1); mint sm = 0; for(int i = 0; n > i; i++){ cin>>B[n-i-1][0]; if(i+1 != n)sm += B[n-i-1][0]; } B[n][0] = sm; mat C = (A.pow(k-n)*B); cout << C[0][0] << " " << (A*C)[n][0] << endl; } void solve2(int n, int k){ vector A(k+1); mint sm = 0; mint rsm = 0; for(int i = 0; n > i; i++){ cin>>A[i]; sm += A[i]; rsm += A[i]; } for(int i = n+1; k >= i; i++){ A[i] = sm; sm -= A[i-n]; sm += A[i]; rsm += A[i]; } cout << A[k] << " " << rsm << endl; } int main(){ long long n,k;cin>>n>>k; if(n <= 30){ solve1(n,k); }else{ solve2(n,k); } return 0; }