#include "bits/stdc++.h" using namespace std; typedef long long ll; typedef pair pii; typedef pair pll; const int INF = 1e9; const ll LINF = 1e18; template ostream& operator << (ostream& out,const pair& o){ out << "(" << o.first << "," << o.second << ")"; return out; } template ostream& operator << (ostream& out,const vector V){ for(int i = 0; i < V.size(); i++){ out << V[i]; if(i!=V.size()-1) out << " ";} return out; } template ostream& operator << (ostream& out,const vector > Mat){ for(int i = 0; i < Mat.size(); i++) { if(i != 0) out << endl; out << Mat[i];} return out; } template ostream& operator << (ostream& out,const map mp){ out << "{ "; for(auto it = mp.begin(); it != mp.end(); it++){ out << it->first << ":" << it->second; if(mp.size()-1 != distance(mp.begin(),it)) out << ", "; } out << " }"; return out; } /* 問題文============================================================ ================================================================= 解説============================================================= ================================================================ */ const ll MOD = 1e9+7; typedef vector vec; typedef vector mat; mat mul(mat&A,mat&B,const ll M){ mat C(A.size(),vec(B[0].size())); for(int i = 0; i < (int)A.size();i++){ for(int k = 0; k < (int)B.size();k++){ for(int j = 0; j < B[0].size();j++){ C[i][j] = (C[i][j] + A[i][k]*B[k][j])%M; } } } return C; } mat pow(mat A,ll n,const ll M){ mat B(A.size(),vec(A.size())); for(int i = 0; i < A.size();i++){ B[i][i] = 1; } while(n > 0){ if(n&1) B= mul(B,A,M); A = mul(A,A,M); n>>=1; } return B; } vector solve(){ vector res; ll N,K; cin >> N >> K; vector A(N); for(auto& in:A) cin >> in; if(K<=1e6){ // testcase01~10 vector F(K+1),S(K+1); for(int i = 0; i < N;i++){ (F[i+1] = A[i])%=MOD; (S[i+1] = S[i] + A[i])%=MOD; } for(ll i = N+1; i <= K;i++){ (F[i] = S[i-1] - S[i-1-N])%=MOD; (S[i] = S[i-1] + F[i])%=MOD; } res = vector{F[K],S[K]}; }else{ // testcase11~20 vector> Mat(N+1,vector(N+1)); for(int i = 0; i <= N;i++) Mat[0][i] = 1; for(int i = 1; i <= N;i++) Mat[1][i] = 1; for(int i = 2; i <= N;i++) Mat[i][i-1] = 1; auto retMat = pow(Mat,K-N,MOD); vector> B(N+1,vector(1)); B[0][0] = accumulate(A.begin(),A.end(),0LL)%MOD; for(int i = 1; i <= N;i++) B[i][0] = A[N-i]; auto ansMat = mul(retMat,B,MOD); res = vector{ansMat[1][0],ansMat[0][0]}; } return res; } int main(void) { cin.tie(0); ios_base::sync_with_stdio(false); cout << solve() << endl; return 0; }