using System; using System.Linq; using System.Collections.Generic; using Debug = System.Diagnostics.Debug; using StringBuilder = System.Text.StringBuilder; using System.Numerics; using Point = System.Numerics.Complex; using Number = System.Double; namespace Program { public class Solver { public void Solve() { var n = sc.Integer(); var l = sc.Integer() * 60; var dt = new int[n]; for (int i = 0; i < n; i++) { dt[i] = sc.Integer() * 60 + sc.Integer(); } if (dt.Sum() <= l) { IO.Printer.Out.WriteLine(n); return; } var sum = dt.Sum(); var seg = new SegmentTree(n, l, dt); var fact = new double[55]; fact[0] = 1; for (int i = 1; i < 55; i++) fact[i] = fact[i - 1] * i; var ret = 0.0; for (int i = 0; i < n; i++) { var dp = seg.data[seg.n + i]; for (int j = 0; j < n; j++) for (int v = Math.Max(0, l - dt[i]); v < l; v++) { double p = dp[j][v]; if (p <= 0) continue; p *= fact[j]; if (n - j - 1 >= 0) p *= fact[n - j - 1]; ret += (j + 1) * p; } } ret /= fact[n]; IO.Printer.Out.WriteLine(ret); } 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 main 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 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, T[] source) { base.Write(format, source.OfType().ToArray()); } public void WriteLine(string format, T[] 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) && !isEof); 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 string ScanLine() { var sb = new StringBuilder(); for (var b = Char(); b != '\n'; b = (char)read()) if (b == 0) break; else if (b != '\r') 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 != 0 && b != '-' && (b < '0' || '9' < b)); if (b == 0) return long.MinValue; 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() { var s = Scan(); return s != "" ? double.Parse(s, CultureInfo.InvariantCulture) : double.NaN; } 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); } } } #endregion #region KnapsackSegmentTere [System.Diagnostics.DebuggerDisplay("Data={ToString()}")] public class SegmentTree { public int n; public Number[][][] data; int[] L, R; 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; } public SegmentTree(int size, int m, int[] a) { n = 1; while (n < size) n <<= 1; data = new Number[n << 1][][]; data[1] = Enumerate(1, x => new Number[m + 1]); data[1][0][0] = 1; L = new int[n << 1]; L[1] = 0; R = new int[n << 1]; R[1] = n; for (int _ = 1; _ < n; _++) { { L[_ << 1] = L[_]; R[(_ << 1)] = L[(_ << 1) + 1] = (L[_] + R[_]) >> 1; R[(_ << 1) + 1] = R[_]; } { var par = data[_].Length; var l = L[(_ << 1) + 1]; var r = Math.Min(size, R[(_ << 1) + 1]); var ret = Enumerate(par + Math.Max(0, r - l), x => new Number[m + 1]); for (int i = 0; i < par; i++) Buffer.BlockCopy(data[_][i], 0, ret[i], 0, m * sizeof(double)); for (int k = l; k < r; k++) { var v = a[k]; for (int i = par - 1; i >= 0; i--) { for (int j = m - v; j >= 0; j--) { if (ret[i][j] <= 0) continue; ret[i + 1][j + v] += ret[i][j]; } } par++; } data[_ << 1] = ret; } { var par = data[_].Length; var l = L[(_ << 1)]; var r = Math.Min(size, R[(_ << 1)]); var ret = Enumerate(par + Math.Max(0, r - l), x => new Number[m + 1]); for (int i = 0; i < par; i++) Buffer.BlockCopy(data[_][i], 0, ret[i], 0, m * sizeof(double)); for (int k = l; k < r; k++) { var v = a[k]; for (int i = par - 1; i >= 0; i--) { for (int j = m - v; j >= 0; j--) { if (ret[i][j] <= 0) continue; ret[i + 1][j + v] += ret[i][j]; } } par++; } data[(_ << 1) + 1] = ret; } } } } #endregion