#include #include #include using namespace std; #define LL long long #define reE(i,a,b) for(auto (i)=(a);(i)<=(b);(i)++) #define rE(i,b) reE(i,0,b) #define reT(i,a,b) for(auto (i)=(a);(i)<(b);(i)++) #define rT(i,b) reT(i,0,b) #define rep(i,a,b) reE(i,a,b); #define rev(i,a,b) for(auto (i)=(b)-1;(i)>=(a);(i)--) #define itr(i,b) for(auto (i)=(b).begin();(i)!=(b).end();++(i)) #define all(b) (b).begin(),(b).end() LL A[1000001]; LL S[1000001]; LL N, K; const LL mod =(LL) 1e9 + 7; #define MAX_LOGN 60 template struct Mr{ vector first; vector C; vector> bin; T zero, one; int M; //n(1,,,2M)をn(1,,,M)に修正、O(M^2) void form(vector &n){ rev(i, M + 1, 2 * M + 1){ reE(j, 1, M)n[i - j] = (n[i - j] + (C[M - j] * n[i])); n[i] = zero; } } //lとrを足し合わせる、O(M^2) void add(vector &l, vector &r, vector &ans){ reE(i, 1, 2 * M)ans[i] = zero; reE(i, 1, M)reE(j, 1, M)ans[i + j] = (ans[i + j] + (l[i] * r[j])); form(ans); } //初期化、O(M*MAX_LOGN) Mr(const vector& f, const vector& c, int m, T e1, T e0){ M = m; first.reserve(M + 1); C.reserve(M); zero = e0, one = e1; first.push_back(zero); rT(i, M){ first.push_back(f[i]); C.push_back(c[i]); } bin.resize(MAX_LOGN); rT(i, MAX_LOGN)bin[i].resize(2 * M + 1); rE(i, 2 * M)bin[0][i] = zero; bin[0][1] = one; reT(i, 1, MAX_LOGN){ add(bin[i - 1], bin[i - 1], bin[i]); } } //N項目の計算、戻り値がTの形であることに注意、O(M^2*logN) T calc(LL n){ n--; vector tmp, result = bin[0]; for (int b = 0; n; b++, n >>= 1) if (1 & n){ tmp = result; add(tmp, bin[b], result); } T ans = zero; reE(i, 1, M)ans = ans + (result[i] * first[i]); return ans; } }; //テンプレート、デフォルトコンストラクタのオーバーロードを忘れない #define MOD 1000000007 struct X{ LL val; X(LL v){ val = v; } X(){ val = 0; } LL operator=(const X &another){ return val = another.val; } LL operator*(const X &another)const{ return (val*another.val) % MOD; } LL operator+(const X &another)const{ return (val + another.val) % MOD; } }; pair case1(){ for (LL i= N + 1; i <= K; i++){ A[i] = (mod + S[i - 1] - S[i - N - 1]) % mod;; S[i] = (A[i] + S[i - 1])%mod; } return make_pair(A[K],S[K]); } pair case2(){ vector f((unsigned)N, 0), s((unsigned)N+1, 0), a((unsigned)N, 1), b((unsigned)N+1, 0); for (int i = 0; i < N; i++){ f[i] = A[i+1]; s[i+1] = S[i + 1]; } b[(unsigned)N] = 2; b[0] = mod - 1; Mr mr(f, a, (int)N, X(1), X(0)); Mr nr(s, b, (int)N + 1, X(1), X(0)); return make_pair(mr.calc(K).val, nr.calc(K+1).val); } int main(void){ cin >> N >> K; for (LL i = 1; i <= N; i++){ cin >> A[i]; S[i] = S[i - 1] + A[i]; S[i] %= mod; } pair res; if (K <= 1000000)res= case1(); else res = case2(); cout << res.first << " " << res.second << endl; return 0; }