/* -*- coding: utf-8 -*- * * 194.cc: No.194 フィボナッチ数列の理解(1) - yukicoder */ #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include using namespace std; /* constant */ const int MAX_N = 10000; const int MAX_K = 1000000; typedef long long ll; const ll MOD = 1000000007; /* typedef */ template struct Vec { int n; vector v; Vec() {} Vec(int _n): n(_n), v(_n, 0) {}; Vec(vector _v): n(_v.size()), v(_v) {}; Vec(int _n, T _as[]): n(_n), v(_n) { for (int i = 0; i < n; i++) v[i] = _as[i]; } T& operator[](int i) { return v[i]; } void print() { for (int i = 0; i < n; i++) printf("%d ", v[i]); putchar('\n'); } }; template struct Matrix { int n; vector > m; Matrix() {} Matrix(int _n): n(_n), m(_n, Vec(_n)) {}; void unit() { for (int i = 0; i < n; i++) m[i][i] = 1; } Vec& operator[](int i) { return m[i]; } Matrix operator*(Matrix& m0) { Matrix mm(n); for (int i = 0; i < n; i++) for (int j = 0; j < n; j++) { mm[i][j] = 0; for (int k = 0; k < n; k++) mm[i][j] = (mm[i][j] + m[i][k] * m0[k][j] % MOD) % MOD; } return mm; } Vec operator*(Vec& v0) { Vec vv(n); for (int i = 0; i < n; i++) for (int j = 0; j < n; j++) vv[i] = (vv[i] + m[i][j] * v0[j] % MOD) % MOD; return vv; } Matrix pow(ll e) { Matrix mm(n), m0 = *this; mm.unit(); while (e > 0) { if ((e & 1) != 0) mm = mm * m0; m0 = m0 * m0; e >>= 1; } return mm; } void trans() { for (int i = 0; i < n; i++) for (int j = i + 1; j < n; j++) swap(m[i][j], m[j][i]); } void print() { for (int i = 0; i < n; i++) m[i].print(); } }; typedef Vec vec; typedef Matrix mat; /* global variables */ ll as[MAX_N]; ll fs[MAX_K], ss[MAX_K]; /* subroutines */ /* main */ int main() { int n; ll k; cin >> n >> k; for (int i = 0; i < n; i++) cin >> as[i]; fs[0] = ss[0] = as[0]; for (int i = 1; i < n; i++) { fs[i] = as[i]; ss[i] = (ss[i - 1] + fs[i]) % MOD; } fs[n] = ss[n - 1]; ss[n] = (ss[n - 1] + fs[n]) % MOD; if (k <= MAX_K) { int ki = k; for (int i = n + 1; i < ki; i++) { fs[i] = (ss[i - 1] + MOD - ss[i - n - 1]) % MOD; ss[i] = (ss[i - 1] + fs[i]) % MOD; } printf("%lld %lld\n", fs[ki - 1], ss[ki - 1]); } else { mat sm(n + 1); for (int i = 0; i < n; i++) sm[i][i + 1] = 1; sm[n][0] = MOD - 1, sm[n][n] = 2; mat pm = sm.pow(k - n - 1); vec sv(n + 1, ss); vec v = pm * sv; ll fk = (v[n] + MOD - v[n - 1]) % MOD; ll sk = v[n]; printf("%lld %lld\n", fk, sk); } return 0; }