#include using namespace std; #define int long long long long gcd(long long a,long long b){ return b ? gcd(b,a%b) : a; } long long lcm(long long a,long long b){ return a / gcd(a,b) * b; } long long mul(long long a,long long b,const long long mod){ return b?(mul(a*2,b/2,mod)+(b&1?a:0))%mod:0; } long long bpow(long long a,long long b,const long long mod){ return (b?bpow(a*a%mod,b/2,mod)*(b&1?a:1):1)%mod; } long long inv(long long a,const long long mod){ return bpow(a,mod-2,mod); } // to overflow /*long long bpow(long long a,long long b,const long long mod){ return (b?mul(bpow(mul(a,a,mod),b/2,mod),(b&1?a:1),mod):1)%mod; }*/ class mInt{ public: static const long long mod = 1000000007; long long v; mInt():v(0){} mInt(long long v):v((v%mod+mod)%mod){} }; mInt& operator += (mInt &a,mInt b){ return a = a.v + b.v; } mInt& operator -= (mInt &a,mInt b){ return a = a.v - b.v; } mInt& operator *= (mInt &a,mInt b){ return a = a.v * b.v; } mInt& operator /= (mInt &a,mInt b){ return a = a.v * inv(b.v,mInt::mod); } mInt operator + (mInt a,mInt b){ return a += b; } mInt operator - (mInt a,mInt b){ return a -= b; } mInt operator * (mInt a,mInt b){ return a *= b; } mInt operator / (mInt a,mInt b){ return a /= b; } ostream& operator<<(ostream& os, const mInt& x){ return os << x.v; } typedef mInt number; const number eps = 0; typedef vector Array; typedef vector matrix; // O( n ) matrix identity(int n) { matrix A(n, Array(n)); for (int i = 0; i < n; ++i) A[i][i] = 1; return A; } // O( n^2 ) Array mul(const matrix &A, const Array &x) { Array y(A.size()); for (int i = 0; i < A.size(); ++i) for (int j = 0; j < A[0].size(); ++j) y[i] = A[i][j] * x[j]; return y; } // O( n^3 ) matrix mul(const matrix &A, const matrix &B) { matrix C(A.size(), Array(B[0].size())); for (int i = 0; i < C.size(); ++i) for (int j = 0; j < C[i].size(); ++j) for (int k = 0; k < A[i].size(); ++k) C[i][j] += A[i][k] * B[k][j]; return C; } // O( n^3 log e ) matrix pow(const matrix &A, int e) { return e == 0 ? identity(A.size()) : e % 2 == 0 ? pow(mul(A, A), e/2) : mul(A, pow(A, e-1)); } #define DIV (1000000007) class BIT : public vector{ public: BIT(int n){ resize(n+1); fill(begin(),end(),0); }; int operator()(int i){ i++; int ans = 0; while(i > 0){ ans = ( ans + (*this)[i] ) % DIV; i -= i & -i; } return ans; } int operator()(int s,int t){ return ( ( (*this)(t) - (*this)(s-1) ) % DIV + DIV ) % DIV; } void add(int i,int x){ i++; int ans = 0; while( i < size() ){ (*this)[i] = ( (*this)[i] + x ) % DIV; i += i & -i; } } void change(int i,int x){ add(i,-(*this)(i,i)); add(i,x); } }; signed main(){ long long sum = 0; long long N,K; cin >> N >> K; if(K <= 1000000){ BIT seg(K+10); for(int i = 1 ; i <= N ; i++){ int w; cin >> w; seg.add(i,w); } for(int i = N+1 ; i <= K ; i++) seg.add(i,seg(i-N,i)); cout << seg(K,K) << " " << seg(K) << endl; }else{ matrix A(N,Array(N)); Array B(N); for(int i = 1 ; i <= N ; i++){ int w; cin >> w; B[i-1] = w; } for(int i = 0 ; i < N ; i++){ for(int j = 0 ; j < N ; j++){ if( i == 0 ) A[i][j] = 1; else A[i][j] = i == j+1; } } int M = K - N; auto m = pow(A,M); mInt sum = 0; for(int j = 0 ; j < N ; j++){ sum += m[0][j] * B[N-j-1]; } mInt res = 0; //for(int i = 0 ; i+1 < N ; i++) // res += B[i]; matrix S(2*N,Array(2*N)); for(int i = 0 ; i < N ; i++){ for(int j = 0 ; j < N ; j++){ S[i][j] = A[i][j]; } } for(int i = 0 ; i < N ; i++){ S[i+N][i] = 1; } for(int i = 0 ; i < N ; i++){ S[i+N][i+N] = 1; } S = pow(S,M+1); for(int i = 0 ; i < N ; i++){ for(int j = 0 ; j < N ; j++) A[i][j] = S[i+N][j]; } for(int j = 0 ; j < N ; j++){ res += j+1 < N ? B[j] : 0; res += A[0][j] * B[N-j-1]; } cout << sum << " " << res << endl; //cout << mul(pow(A,K-1),B) << endl; } }