package q8xx; import java.io.ByteArrayInputStream; import java.io.IOException; import java.io.InputStream; import java.io.PrintWriter; import java.util.Arrays; import java.util.InputMismatchException; // O(N^3) public class Q874_3 { InputStream is; PrintWriter out; String INPUT = ""; // String INPUT = "4 7 1 2 2 1 2 3 3 2 2 4 4 2 2 2"; boolean[][] shrink(boolean[][] ng) { int n = ng.length; int[] outdeg = new int[n]; int[] indeg = new int[n]; for(int i = 0;i < n;i++){ for(int j = 0;j < n;j++){ if(!ng[i][j]){ outdeg[i]++; indeg[j]++; } } } int[] map = new int[n]; Arrays.fill(map, -1); int p = 0; for(int i = 0;i < n;i++){ if(!(outdeg[i] == 0 && indeg[i] == 0)){ map[i] = p++; } } boolean[][] nng = new boolean[p][p]; for(int i = 0;i < n;i++){ for(int j = 0;j < n;j++){ if(ng[i][j] && map[i] != -1 && map[j] != -1){ nng[map[i]][map[j]] = true; } } } return nng; } int mod = 1000000007; void solve() { int n = ni(), m = ni(); if(n*n == m){ out.println(1); return; } int on = n; boolean[][] ng = new boolean[n][n]; for(int i = 0;i < m;i++){ int f = ni()-1, t = ni()-1; ng[f][t] = true; } ng = shrink(ng); n = ng.length; int[] outdeg = new int[n]; int[] indeg = new int[n]; for(int i = 0;i < n;i++){ for(int j = 0;j < n;j++){ if(!ng[i][j]){ outdeg[i]++; indeg[j]++; } } } // connectivity DJSet ds = new DJSet(n); for(int i = 0;i < n;i++){ for(int j = 0;j < n;j++){ if(!ng[i][j]){ ds.union(i, j); } } } for(int i = 0;i < n;i++){ for(int j = i+1;j < n;j++){ if( (outdeg[i] >= 1 || indeg[i] >= 1) && (outdeg[j] >= 1 || indeg[j] >= 1) ){ if(!ds.equiv(i, j)){ out.println(0); return; } } } } int src = -1, sink = -1; for(int i = 0;i < n;i++){ if(outdeg[i] == indeg[i])continue; if(outdeg[i] == indeg[i]+1 && src == -1){ src = i; continue; } if(outdeg[i] == indeg[i]-1 && sink == -1){ sink = i; continue; } out.println(0); return; } int[][] M = new int[n][n]; for(int i = 0;i < n;i++){ for(int j = 0;j < n;j++){ if(!ng[i][j]){ if(i != j){ M[i][j] = mod-1; M[i][i]++; } } } } // for(int[] row : M){ // tr(row); // } int[][] MM = new int[n+1][n+1]; for(int i = 0;i < n;i++){ for(int j = 0;j < n;j++){ MM[i+1][j+1] = M[i][j]+1; if(MM[i+1][j+1] == mod)MM[i+1][j+1] = 0; } } MM[0][0] = 1; for(int i = 1;i < n+1;i++)MM[0][i] = mod-1; for(int i = 1;i < n+1;i++)MM[i][0] = mod-1; for(int i = 0;i < n+1;i++){ long s = 0; for(int j = 1;j < n;j++)s += MM[i][j]; s %= mod; s = s * invl(n, mod) % mod; MM[i][0] += s; if(MM[i][0] >= mod)MM[i][0] -= mod; } // for(int[] row : MM){ // tr(row); // } if(src == -1){ out.println(numEulerianCircuit(MM, outdeg, indeg) * (on*on-m) % mod); }else{ if(--MM[sink+1][src+1] < 0)MM[sink+1][src+1] += mod; if(--M[sink][src] < 0)M[sink][src] += mod; MM[sink+1][sink+1]++; outdeg[sink]++; indeg[src]++; long nec = numEulerianCircuit(MM, outdeg, indeg); out.println(nec * invl(mod-M[sink][src], mod) % mod); } } long numEulerianCircuit(int[][] M, int[] outdeg, int[] indeg) { int n = M.length; long[] F = new long[n+2]; F[0] = 1; for(int i = 1;i <= n;i++)F[i] = F[i-1] * i % mod; long ec = 1; for(int i = 0;i < outdeg.length;i++){ ec = ec * F[outdeg[i]-1] % mod; } int[][] Q = new int[n-1][n-1]; for(int i = 0;i < n-1;i++){ for(int j = 0;j < n-1;j++){ Q[i][j] = M[i][j]; } } // tr(n-1); long det = det(Q, mod); // tr(det); return ec * det % mod; } public static class DJSet { public int[] upper; public DJSet(int n) { upper = new int[n]; Arrays.fill(upper, -1); } public int root(int x) { return upper[x] < 0 ? x : (upper[x] = root(upper[x])); } public boolean equiv(int x, int y) { return root(x) == root(y); } public boolean union(int x, int y) { x = root(x); y = root(y); if (x != y) { if (upper[y] < upper[x]) { int d = x; x = y; y = d; } upper[x] += upper[y]; upper[y] = x; } return x == y; } public int count() { int ct = 0; for (int u : upper) if (u < 0) ct++; return ct; } } public static long det(int[][] a, int mod) { int n = a.length; long ret = 1; for(int i = 0;i < n;i++){ int pivot = -1; for(int j = i;j < n;j++){ if(a[j][i] == 0)continue; pivot = j; break; } if(pivot == -1)return 0L; // swap rows if(i != pivot){ {int[] d = a[i]; a[i] = a[pivot]; a[pivot] = d;} ret = mod-ret; } long inv = invl(a[i][i], mod); for(int r = i+1;r < n;r++){ if(a[r][i] != 0){ // tr(i, r); long mul = -a[r][i] * inv % mod; if(mul < 0)mul += mod; for(int c = i+1;c < n;c++){ a[r][c] = (int)((a[r][c] + a[i][c] * mul) % mod); } } } ret = ret * a[i][i] % mod; } if(ret < 0)ret += mod; return ret; } public static long invl(long a, long mod) { long b = mod; long p = 1, q = 0; while (b > 0) { long c = a / b; long d; d = a; a = b; b = d % b; d = p; p = q; q = d - c * q; } return p < 0 ? p + mod : p; } void run() throws Exception { is = INPUT.isEmpty() ? System.in : new ByteArrayInputStream(INPUT.getBytes()); out = new PrintWriter(System.out); long s = System.currentTimeMillis(); solve(); out.flush(); if(!INPUT.isEmpty())tr(System.currentTimeMillis()-s+"ms"); // Thread t = new Thread(null, null, "~", Runtime.getRuntime().maxMemory()){ // @Override // public void run() { // long s = System.currentTimeMillis(); // solve(); // out.flush(); // if(!INPUT.isEmpty())tr(System.currentTimeMillis()-s+"ms"); // } // }; // t.start(); // t.join(); } public static void main(String[] args) throws Exception { new Q874_3().run(); } private byte[] inbuf = new byte[1024]; private int lenbuf = 0, ptrbuf = 0; private int readByte() { if(lenbuf == -1)throw new InputMismatchException(); if(ptrbuf >= lenbuf){ ptrbuf = 0; try { lenbuf = is.read(inbuf); } catch (IOException e) { throw new InputMismatchException(); } if(lenbuf <= 0)return -1; } return inbuf[ptrbuf++]; } private boolean isSpaceChar(int c) { return !(c >= 33 && c <= 126); } private int skip() { int b; while((b = readByte()) != -1 && isSpaceChar(b)); return b; } private double nd() { return Double.parseDouble(ns()); } private char nc() { return (char)skip(); } private String ns() { int b = skip(); StringBuilder sb = new StringBuilder(); while(!(isSpaceChar(b))){ // when nextLine, (isSpaceChar(b) && b != ' ') sb.appendCodePoint(b); b = readByte(); } return sb.toString(); } private char[] ns(int n) { char[] buf = new char[n]; int b = skip(), p = 0; while(p < n && !(isSpaceChar(b))){ buf[p++] = (char)b; b = readByte(); } return n == p ? buf : Arrays.copyOf(buf, p); } private int[] na(int n) { int[] a = new int[n]; for(int i = 0;i < n;i++)a[i] = ni(); return a; } private long[] nal(int n) { long[] a = new long[n]; for(int i = 0;i < n;i++)a[i] = nl(); return a; } private char[][] nm(int n, int m) { char[][] map = new char[n][]; for(int i = 0;i < n;i++)map[i] = ns(m); return map; } private int[][] nmi(int n, int m) { int[][] map = new int[n][]; for(int i = 0;i < n;i++)map[i] = na(m); return map; } private int ni() { return (int)nl(); } private long nl() { long num = 0; int b; boolean minus = false; while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-')); if(b == '-'){ minus = true; b = readByte(); } while(true){ if(b >= '0' && b <= '9'){ num = num * 10 + (b - '0'); }else{ return minus ? -num : num; } b = readByte(); } } private static void tr(Object... o) { System.out.println(Arrays.deepToString(o)); } }