using System; using System.Collections.Generic; using System.Linq; using Debug = System.Diagnostics.Debug; using Watch = System.Diagnostics.Stopwatch; using StringBuilder = System.Text.StringBuilder; using System.Numerics; namespace Program { public class Solver { public void Solve() { var n = sc.Integer(); var k = sc.Long(); var a = sc.Integer(n); var dp = new ModInteger[Math.Min(1000050, k + 50)]; var cum = new ModInteger[Math.Min(1000050, k + 50)]; for (int i = 0; i < n; i++) dp[i + 1] = a[i]; for (int i = 1; i <= n; i++) cum[i] = dp[i] + cum[i - 1]; if (n > 30) { for (int i = n + 1; i <= k; i++) { dp[i] = cum[i - 1] - cum[i - 1 - n]; cum[i] = dp[i] + cum[i - 1]; } IO.Printer.Out.WriteLine("{0} {1}", dp[k], cum[k]); } else { var mat = new FastModMatrix(n + 1, n + 1); for (int i = 0; i < n; i++) mat[0, i] = 1; for (int i = 1; i < n; i++) mat[i, i - 1] = 1; mat[n, n - 1] = mat[n, n] = 1; var res = FastModMatrix.Pow(mat, k - 1); ModInteger ans = 0; ModInteger sum = 0; for (int i = 0; i < n; i++) { ans += res[n - 1, i] * dp[n - i]; sum += res[n, i] * dp[n - i]; } IO.Printer.Out.WriteLine("{0} {1}", ans, sum+ans); } } public IO.StreamScanner sc = new IO.StreamScanner(Console.OpenStandardInput()); static T[] Enumerate(int n, Func f) { var a = new T[n]; for (int i = 0; i < n; ++i) a[i] = f(i); return a; } static public void Swap(ref T a, ref T b) { var tmp = a; a = b; b = tmp; } } } #region Ex namespace Program.IO { using System.IO; using System.Text; using System.Globalization; public class Printer : StreamWriter { static Printer() { Out = new Printer(Console.OpenStandardOutput()) { AutoFlush = false }; } public static Printer Out { get; set; } public override IFormatProvider FormatProvider { get { return CultureInfo.InvariantCulture; } } public Printer(System.IO.Stream stream) : base(stream, new UTF8Encoding(false, true)) { } public Printer(System.IO.Stream stream, Encoding encoding) : base(stream, encoding) { } public void Write(string format, IEnumerable source) { base.Write(format, source.OfType().ToArray()); } public void WriteLine(string format, IEnumerable source) { base.WriteLine(format, source.OfType().ToArray()); } } public class StreamScanner { public StreamScanner(Stream stream) { str = stream; } public readonly Stream str; private readonly byte[] buf = new byte[1024]; private int len, ptr; public bool isEof = false; public bool IsEndOfStream { get { return isEof; } } private byte read() { if (isEof) return 0; if (ptr >= len) { ptr = 0; if ((len = str.Read(buf, 0, 1024)) <= 0) { isEof = true; return 0; } } return buf[ptr++]; } public char Char() { byte b = 0; do b = read(); while (b < 33 || 126 < b); return (char)b; } public string Scan() { var sb = new StringBuilder(); for (var b = Char(); b >= 33 && b <= 126; b = (char)read()) sb.Append(b); return sb.ToString(); } public long Long() { if (isEof) return long.MinValue; long ret = 0; byte b = 0; var ng = false; do b = read(); while (b != '-' && (b < '0' || '9' < b)); if (b == '-') { ng = true; b = read(); } for (; true; b = read()) { if (b < '0' || '9' < b) return ng ? -ret : ret; else ret = ret * 10 + b - '0'; } } public int Integer() { return (isEof) ? int.MinValue : (int)Long(); } public double Double() { return double.Parse(Scan(), CultureInfo.InvariantCulture); } private T[] enumerate(int n, Func f) { var a = new T[n]; for (int i = 0; i < n; ++i) a[i] = f(); return a; } public char[] Char(int n) { return enumerate(n, Char); } public string[] Scan(int n) { return enumerate(n, Scan); } public double[] Double(int n) { return enumerate(n, Double); } public int[] Integer(int n) { return enumerate(n, Integer); } public long[] Long(int n) { return enumerate(n, Long); } } } static class Ex { static public string AsString(this IEnumerable ie) { return new string(System.Linq.Enumerable.ToArray(ie)); } static public string AsJoinedString(this IEnumerable ie, string st = " ") { return string.Join(st, ie); } static public void Main() { var solver = new Program.Solver(); solver.Solve(); Program.IO.Printer.Out.Flush(); } } #endregion #region ModNumber public struct ModInteger { public const long Mod = (long)1e9 + 7; public long num; public ModInteger(long n) : this() { num = n % Mod; } public override string ToString() { return num.ToString(); } public static ModInteger operator +(ModInteger l, ModInteger r) { var n = l.num + r.num; if (n >= Mod)n -= Mod; return new ModInteger(n); } public static ModInteger operator -(ModInteger l, ModInteger r) { var n = l.num - r.num; if (n < 0)n += Mod; return new ModInteger(n); } public static ModInteger operator *(ModInteger l, ModInteger r) { return new ModInteger((l.num * r.num) % Mod); } public static implicit operator ModInteger(long n) { return new ModInteger(n); } } #endregion #region ModMatrix public class FastModMatrix { int row, col; public ulong[] mat; const int sz = 18; public ModInteger this[int r, int c] { get { return new ModInteger((long)mat[r * col + c]); } set { mat[r * col + c] = (ulong)value.num; } } public FastModMatrix(int r, int c) { if (r % sz > 0) r += sz - r % sz; if (c % sz > 0) c += sz - c % sz; row = r; col = c; mat = new ulong[row * col]; } public static FastModMatrix operator +(FastModMatrix l, FastModMatrix r) { check(l, r); var ret = new FastModMatrix(l.row, l.col); for (int i = 0; i < l.row; i++) for (int j = 0; j < l.col; j++) { ret.mat[i * ret.col + j] = l.mat[i * l.col + j] + r.mat[i * r.col + j]; if (ret.mat[i * ret.col + j] >= ModInteger.Mod) ret.mat[i * ret.col + j] -= ModInteger.Mod; } return ret; } //ループアンローリングパワーで高速化(剰余演算回数を減らしている) public static FastModMatrix operator *(FastModMatrix l, FastModMatrix r) { checkMul(l, r); var ret = new FastModMatrix(l.row, l.col); for (int i = 0; i < l.row; i++) for (int k = 0; k < l.row; k += sz) for (int j = 0; j < l.col; j++) ret.mat[i * l.col + j] = (ret.mat[i * l.col + j] + l.mat[i * l.col + k] * r.mat[k * l.col + j] + l.mat[i * l.col + k + 1] * r.mat[(k + 1) * l.col + j] + l.mat[i * l.col + k + 2] * r.mat[(k + 2) * l.col + j] + l.mat[i * l.col + k + 3] * r.mat[(k + 3) * l.col + j] + l.mat[i * l.col + k + 4] * r.mat[(k + 4) * l.col + j] + l.mat[i * l.col + k + 5] * r.mat[(k + 5) * l.col + j] + l.mat[i * l.col + k + 6] * r.mat[(k + 6) * l.col + j] + l.mat[i * l.col + k + 7] * r.mat[(k + 7) * l.col + j] + l.mat[i * l.col + k + 8] * r.mat[(k + 8) * l.col + j] + l.mat[i * l.col + k + 9] * r.mat[(k + 9) * l.col + j] + l.mat[i * l.col + k + 10] * r.mat[(k + 10) * l.col + j] + l.mat[i * l.col + k + 11] * r.mat[(k + 11) * l.col + j] + l.mat[i * l.col + k + 12] * r.mat[(k + 12) * l.col + j] + l.mat[i * l.col + k + 13] * r.mat[(k + 13) * l.col + j] + l.mat[i * l.col + k + 14] * r.mat[(k + 14) * l.col + j] + l.mat[i * l.col + k + 15] * r.mat[(k + 15) * l.col + j] + l.mat[i * l.col + k + 16] * r.mat[(k + 16) * l.col + j] + l.mat[i * l.col + k + 17] * r.mat[(k + 17) * l.col + j]) % ModInteger.Mod; return ret; } public static FastModMatrix Pow(FastModMatrix m, long n) { var ret = new FastModMatrix(m.row, m.col); for (int i = 0; i < m.row; i++) ret.mat[i * m.col + i] = 1; for (; n > 0; m *= m, n >>= 1) if ((n & 1) == 1) ret = ret * m; return ret; } public static FastModMatrix Trans(FastModMatrix m) { var ret = new FastModMatrix(m.col, m.row); for (int i = 0; i < m.row; i++) for (int j = 0; j < m.col; j++) ret.mat[j * m.col + i] = m.mat[i * m.col + j]; return ret; } [System.Diagnostics.Conditional("DEBUG")] static private void check(FastModMatrix a, FastModMatrix b) { if (a.row != b.row || a.col != b.col) throw new Exception("row and col have to be same."); } [System.Diagnostics.Conditional("DEBUG")] static private void checkMul(FastModMatrix a, FastModMatrix b) { if (a.col != b.row) throw new Exception("row and col have to be same."); } } #endregion