#include using namespace std; #define int long long #define double long double #define FOR(i, a, b) for(ll i = (a); i < (b); ++i) #define FORR(i, a, b) for(ll i = (a); i > (b); --i) #define REP(i, n) for(ll i = 0; i < (n); ++i) #define REPR(i, n) for(ll i = n; i >= 0; i--) #define FOREACH(x, a) for(auto &(x) : (a)) #define VECCIN(x) \ for(auto &youso_ : (x)) cin >> youso_ #define bitcnt(x) __builtin_popcount(x) #define lbit(x) __builtin_ffsll(x) #define rbit(x) __builtin_clzll(x) #define SZ(x) ((ll)(x).size()) #define fi first #define se second #define All(a) (a).begin(), (a).end() #define rAll(a) (a).rbegin(), (a).rend() template inline T IN() { T x; cin >> x; return (x); } inline void CIN() {} template inline void CIN(Head &&head, Tail &&... tail) { cin >> head; CIN(move(tail)...); } #define CCIN(...) \ char __VA_ARGS__; \ CIN(__VA_ARGS__) #define DCIN(...) \ double __VA_ARGS__; \ CIN(__VA_ARGS__) #define LCIN(...) \ ll __VA_ARGS__; \ CIN(__VA_ARGS__) #define SCIN(...) \ string __VA_ARGS__; \ CIN(__VA_ARGS__) #define Yes(a) cout << (a ? "Yes" : "No") << "\n" #define YES(a) cout << (a ? "YES" : "NO") << "\n" #define Printv(v) \ { \ FOREACH(x, v) { cout << x << " "; } \ cout << "\n"; \ } template inline void eputs(T s) { cout << s << "\n"; exit(0); } template void Fill(A (&array)[N], const T &val) { std::fill((T *)array, (T *)(array + N), val); } template using PQG = priority_queue, greater>; template using PQ = priority_queue; typedef long long ll; typedef vector VL; typedef vector VVL; typedef pair PL; typedef vector VPL; typedef vector VB; typedef vector VD; typedef vector VS; const int INF = 1e9; const int MOD = 1e9 + 7; // const int MOD = 998244353; const ll LINF = 1e18; // const double PI = atan(1.0) * 4.0; const ll dx[] = {1, 1, 0, -1, -1, -1, 0, 1}; const ll dy[] = {0, 1, 1, 1, 0, -1, -1, -1}; #define PI 3.141592653589793238 // 1000000007 で割ったあまりを扱う構造体 template struct Fp { long long val; constexpr Fp(long long v = 0) noexcept : val(v % MOD) { if(val < 0) v += MOD; } constexpr int getmod() { return MOD; } constexpr Fp operator-() const noexcept { return val ? MOD - val : 0; } constexpr Fp operator+(const Fp &r) const noexcept { return Fp(*this) += r; } constexpr Fp operator-(const Fp &r) const noexcept { return Fp(*this) -= r; } constexpr Fp operator*(const Fp &r) const noexcept { return Fp(*this) *= r; } constexpr Fp operator/(const Fp &r) const noexcept { return Fp(*this) /= r; } constexpr Fp &operator+=(const Fp &r) noexcept { val += r.val; if(val >= MOD) val -= MOD; return *this; } constexpr Fp &operator-=(const Fp &r) noexcept { val -= r.val; if(val < 0) val += MOD; return *this; } constexpr Fp &operator*=(const Fp &r) noexcept { val = val * r.val % MOD; return *this; } constexpr Fp &operator/=(const Fp &r) noexcept { long long a = r.val, b = MOD, u = 1, v = 0; while(b) { long long t = a / b; a -= t * b; swap(a, b); u -= t * v; swap(u, v); } val = val * u % MOD; if(val < 0) val += MOD; return *this; } constexpr bool operator==(const Fp &r) const noexcept { return this->val == r.val; } constexpr bool operator!=(const Fp &r) const noexcept { return this->val != r.val; } friend constexpr ostream &operator<<(ostream &os, const Fp &x) noexcept { return os << x.val; } friend constexpr istream &operator>>(istream &is, Fp &x) noexcept { return is >> x.val; } friend constexpr Fp modpow(const Fp &a, long long n) noexcept { if(n == 0) return 1; auto t = modpow(a, n / 2); t = t * t; if(n & 1) t = t * a; return t; } }; using mint = Fp; vector kitamasa(const vector &c, const vector &u, const vector &v) { size_t k = c.size(); vector r(2 * k - 1); for(int i = 0; i < k; i++) for(int j = 0; j < k; j++) r[i + j] += u[i] * v[j]; for(int i = 2 * k - 2; i >= k; i--) for(int j = 0; j < k; j++) r[i - k + j] += r[i] * c[j]; r.resize(k); return r; } signed main() { LCIN(K, M); vector sum(K + 1); REP(i, K) sum[i + 1] += (mint)IN() + sum[i]; ll dep = log2(M); if(K <= 30) { vector C(K + 1); C[K] = 2, C[0] -= 1; vector> b(dep + 1, vector(K + 1)); b[0][1] = 1; REP(i, dep) { b[i + 1] = kitamasa(C, b[i], b[i]); } vector now(K + 1); now[0] = 1; REP(i, dep + 1) { if(M >> i & 1) { now = kitamasa(C, now, b[i]); } } mint ans = 0; REP(i, K + 1) { ans += now[i] * sum[i]; } M--; now.assign(K + 1, 0); now[0] = 1; REP(i, dep + 1) { if(M >> i & 1) { now = kitamasa(C, now, b[i]); } } mint pre = 0; REP(i, K + 1) { pre += now[i] * sum[i]; } cout << (mint)ans - pre << " " << ans << "\n"; } else { sum.resize(M + 1); FOR(i, K + 1, M + 1) { sum[i] = sum[i - 1] * 2 - sum[i - K - 1]; } cout << sum[M] - sum[M - 1] << " " << sum[M] << "\n"; } }