using System; using System.IO; using System.Linq; using System.Text; using System.Collections.Generic; using System.Diagnostics; using System.Numerics; using Enu = System.Linq.Enumerable; class Program { static readonly int SmallN = (int)1e6; static readonly int Mod = (int)1e9 + 7; public void Solve() { int L = Reader.Int(); long N = Reader.Long(); var F = new[] { 0 }.Concat(Reader.IntArray(L)).Concat(new int[SmallN]).ToArray(); var S = new int[SmallN + 1]; for (int i = 1; i <= L; i++) S[i] = (F[i] + S[i - 1]) % Mod; if (N <= SmallN) { for (int i = L + 1; i <= N; i++) { F[i] = (S[i - 1] - S[i - L - 1] + Mod) % Mod; S[i] = (F[i] + S[i - 1]) % Mod; } Console.WriteLine(F[N] + " " + S[N]); } else { var M = new Matrix(L, L, Mod); for (int c = 0; c < L; c++) M[0, c] = 1; for (int r = 1; r < L; r++) M[r, r - 1] = 1; long[] X = F.Skip(1).Take(L).Select(x => (long)x).ToArray(); long f, s; LinearRecurrenceRelationSum(M, X, N, out f, out s); Console.WriteLine(f + " " + s); } } // Xn = X[N], Sum = X[1] + X[2] + ... + X[N] public void LinearRecurrenceRelationSum(Matrix A, long[] X, long N, out long Xn, out long Sum) { int H = A.H; var M = new Matrix(H * 2, H * 2, Mod); var IO = new Matrix(H * 2, H, Mod); for (int r = 0; r < H; r++) for (int c = 0; c < H; c++) M[r, c] = A[r, c]; for (int i = 0; i < H; i++) M[H + i, i] = M[H + i, H + i] = IO[i, i] = 1; M = M.Power(N - H + 1) * IO; for (int i = 0; i < H; i++) M[H + i, i] -= 1; Xn = Sum = 0; for (int i = 0; i < H; i++) { Xn = (Xn + M[1, i] * X[H - 1 - i]) % Mod; Sum = (Sum + X[i]) % Mod; Sum = (Sum + M[H, i] * X[H - 1 - i]) % Mod; } } public class Matrix { public readonly int H, W; public readonly long Mod; private readonly long[][] M; public long this[int r, int c] { get { return M[r][c]; } set { M[r][c] = value >= 0 ? value % Mod : value % Mod + Mod; } } public Matrix(int h, int w, long mod) { H = h; W = w; Mod = mod; M = new long[h][]; for (int r = 0; r < H; r++) M[r] = new long[w]; } public Matrix(long[] vec, long mod) { H = vec.Length; W = 1; Mod = mod; M = new long[H][]; for (int r = 0; r < H; r++) { M[r] = new long[1]; this[r, 0] = vec[r]; } } public Matrix(int[] vec, long mod) { H = vec.Length; W = 1; Mod = mod; M = new long[H][]; for (int r = 0; r < H; r++) { M[r] = new long[1]; this[r, 0] = vec[r]; } } public static Matrix operator +(Matrix A, Matrix B) { Debug.Assert(A.H == B.H && A.W == B.W && A.Mod == B.Mod); var res = A.Clone(); for (int r = 0; r < res.H; r++) for (int c = 0; c < res.W; c++) if ((res.M[r][c] += B.M[r][c]) >= A.Mod) res.M[r][c] -= A.Mod; return res; } public static Matrix operator *(Matrix A, Matrix B) { Debug.Assert(A.W == B.H && A.Mod == B.Mod); long mod = A.Mod; var res = new Matrix(A.H, B.W, mod); int h = res.H, w1 = A.W, w2 = res.W; long[][] C = res.M, a = A.M, b = B.M; for (int r = 0; r < h; r++) for (int i = 0; i < w1; i++) for (int c = 0; c < w2; c++) if ((C[r][c] += a[r][i] * b[i][c] % mod) >= mod) C[r][c] -= mod; return res; } public Matrix Power(long pow) { Debug.Assert(H == W); var A = Clone(); var res = new Matrix(H, W, Mod); for (int i = 0; i < H; i++) res[i, i] = 1; while (pow > 0) { if ((pow & 1) == 1) res = res * A; A = A * A; pow >>= 1; } return res; } public Matrix Clone() { var res = new Matrix(H, W, Mod); for (int r = 0; r < H; r++) Array.Copy(M[r], res.M[r], res.W); return res; } public override string ToString() { var s = new StringBuilder(); int L = 2; for (int r = 0; r < H; r++) for (int c = 0; c < W; c++) L = Math.Max(L, this[r, c].ToString().Length); for (int r = 0; r < H; r++) { for (int c = 0; c < W; c++) s.Append(this[r, c].ToString().PadLeft(L + 1, ' ')); s.AppendLine(); } return s.ToString(); } } } class Entry { static void Main() { new Program().Solve(); } } class Reader { private static TextReader reader = Console.In; private static readonly char[] separator = { ' ' }; private static readonly StringSplitOptions op = StringSplitOptions.RemoveEmptyEntries; private static string[] A = new string[0]; private static int i; private static void Init() { A = new string[0]; } public static void Set(TextReader r) { reader = r; Init(); } public static void Set(string file) { reader = new StreamReader(file); Init(); } public static bool HasNext() { return CheckNext(); } public static string String() { return Next(); } public static int Int() { return int.Parse(Next()); } public static long Long() { return long.Parse(Next()); } public static double Double() { return double.Parse(Next()); } public static int[] IntLine() { return Array.ConvertAll(Split(Line()), int.Parse); } public static int[] IntArray(int N) { return Enu.Range(0, N).Select(i => Int()).ToArray(); } public static int[][] IntTable(int H) { return Enu.Range(0, H).Select(i => IntLine()).ToArray(); } public static string[] StringArray(int N) { return Enu.Range(0, N).Select(i => Line()).ToArray(); } public static string Line() { return reader.ReadLine().Trim(); } private static string[] Split(string s) { return s.Split(separator, op); } private static string Next() { CheckNext(); return A[i++]; } private static bool CheckNext() { if (i < A.Length) return true; string line = reader.ReadLine(); if (line == null) return false; if (line == "") return CheckNext(); A = Split(line); i = 0; return true; } }