Problem:
Score : 1600 points

Problem Statement

There is a directed graph G with N vertices and M edges.
The vertices are numbered 1 through N, and the edges are numbered 1 through M.
Edge i is directed from x_i to y_i.
Here, x_i < y_i holds.
Also, there are no multiple edges in G.

Consider selecting a subset of the set of the M edges in G, and removing these edges from G to obtain another graph G'.
There are 2^M different possible graphs as G'.

Alice and Bob play against each other in the following game played on G'.
First, place two pieces on vertices 1 and 2, one on each.
Then, starting from Alice, Alice and Bob alternately perform the following operation:

Select an edge i such that there is a piece placed on vertex x_i, and move the piece to vertex y_i (if there are two pieces on vertex x_i, only move one). The two pieces are allowed to be placed on the same vertex.

The player loses when he/she becomes unable to perform the operation.
We assume that both players play optimally.

Among the 2^M different possible graphs as G', how many lead to Alice's victory?
Find the count modulo 10^9+7.

Constraints

2 ≤ N ≤ 15

1 ≤ M ≤ N(N-1)/2

1 ≤ x_i < y_i ≤ N

All (x_i,\ y_i) are distinct.

Input

Input is given from Standard Input in the following format:

N M
x_1 y_1
x_2 y_2
:
x_M y_M

Output

Print the number of G' that lead to Alice's victory, modulo 10^9+7.

Sample Input 1

2 1
1 2

Sample Output 1

1

The figure below shows the two possible graphs as G'.
A graph marked with ○ leads to Alice's victory, and a graph marked with × leads to Bob's victory.

Sample Input 2

3 3
1 2
1 3
2 3

Sample Output 2

6

The figure below shows the eight possible graphs as G'.

Sample Input 3

4 2
1 3
2 4

Sample Output 3

2

Sample Input 4

5 10
2 4
3 4
2 5
2 3
1 2
3 5
1 3
1 5
4 5
1 4

Sample Output 4

816

Solution in C# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.Linq;
using System.Collections.Generic;
using Debug = System.Diagnostics.Debug;
using SB = System.Text.StringBuilder;
//using System.Numerics;
using Number = System.Int64;
using static System.Math;
//using static MathEx;
//using P = System.Collections.Generic.KeyValuePair<int, int>;

namespace Program
{
    public class Solver
    {
        public void Solve()
        {
            var n = ri;
            var m = ri;
            var g = new int[n];
            var rg = new int[n];
            var dp = new long[1 << n];
            for (int i = 0; i < 1 << n; i++)
                dp[i] = -1;
            dp[0] = 1;
            for (int i = 0; i < m; i++)
            {
                var x = ri - 1;
                var y = ri - 1;
                g[x] |= 1 << y;
                rg[y] |= 1 << x;
            }
            var C = new int[1 << n, n];
            for (int i = 0; i < 1 << n; i++)
                for (int j = 0; j < n; j++)
                {
                    C[i, j] = (1 << PopCount(g[j] & i)) - 1;
                    C[i, j] *= 1 << PopCount(rg[j] & i);
                }
            const long MOD = (long)1e9 + 7;
            Func<int, long> f = null;
            f = (mask) =>
              {
                  if (dp[mask] >= 0) return dp[mask];
                  long ret = 0;
                  for (int sub = mask; sub > 0; sub = (sub - 1) & mask)
                  {
                      if ((sub & 3) == 3) continue;
                      var rem = mask ^ sub;
                      var ok = true;
                      long pat = 1;
                      for (int i = 0; i < n; i++)
                      {
                          if ((mask >> i & 1) == 1) continue;
                          pat = (pat * C[sub, i]) % MOD;
                      }
                      if (ok)
                          ret = (ret + pat * f(rem)) % MOD;
                  }
                  return dp[mask] = ret;
              };
            IO.Printer.Out.WriteLine(f((1 << n) - 1));

        }
        int PopCount(int x)
        {
            var ret = 0;
            while (x != 0)
            {
                ret += x & 1;
                x /= 2;
            }
            return ret;
        }
        //*
        int ri => sc.Integer();
        long rl => sc.Long();
        double rd => sc.Double();
        string rs => sc.Scan();
        char rc => sc.Char();

        [System.Diagnostics.Conditional("DEBUG")]
        void put(params object[] a) => Debug.WriteLine(string.Join(" ", a));

        //*/
        public IO.StreamScanner sc = new IO.StreamScanner(Console.OpenStandardInput());

        static T[] Enumerate<T>(int n, Func<int, T> f)
        {
            var a = new T[n];
            for (int i = 0; i < n; ++i) a[i] = f(i);
            return a;
        }
        static void Swap<T>(ref T a, ref T b)
        {
            var tmp = a;
            a = b;
            b = tmp;
        }
    }
}

#region main

static class Ex
{
    public static string AsString(this IEnumerable<char> ie)
    {
        return new string(ie.ToArray());
    }

    public static string AsJoinedString<T>(this IEnumerable<T> ie, string st = " ")
    {
        return string.Join(st, ie);
    }

    public static 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(Stream stream) : base(stream, new UTF8Encoding(false, true))
        {
        }

        public Printer(Stream stream, Encoding encoding) : base(stream, encoding)
        {
        }

        public void Write<T>(string format, T[] source)
        {
            base.Write(format, source.OfType<object>().ToArray());
        }

        public void WriteLine<T>(string format, T[] source)
        {
            base.WriteLine(format, source.OfType<object>().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;

        public bool IsEndOfStream
        {
            get { return isEof; }
        }

        private byte read()
        {
            if (isEof) return 0;
            if (ptr < len) return buf[ptr++];
            ptr = 0;
            if ((len = str.Read(buf, 0, 1024)) > 0) return buf[ptr++];
            isEof = true;
            return 0;
        }

        public char Char()
        {
            byte b;
            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;
            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 (; ; b = read())
            {
                if (b < '0' || '9' < b)
                    return ng ? -ret : ret;
                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;
        }

        static T[] enumerate<T>(int n, Func<T> 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