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#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
#define INF 1000000000
#define INFl 1000000000000000000
#define all(x) x.begin(), x.end()
#define sajz(x) (int)x.size()
#define pb push_back
#define se second
#define fi first
#define yes puts("YES")
#define no puts("NO")
#define erase_duplicates(x) {sort(all(x));(x).resize(distance((x).begin(), unique(all(x))));}
using namespace std;
using namespace __gnu_pbds;
void __print(int x) {cerr << x;}
void __print(long x) {cerr << x;}
void __print(long long x) {cerr << x;}
void __print(unsigned x) {cerr << x;}
void __print(unsigned long x) {cerr << x;}
void __print(unsigned long long x) {cerr << x;}
void __print(float x) {cerr << x;}
void __print(double x) {cerr << x;}
void __print(long double x) {cerr << x;}
void __print(char x) {cerr << '\'' << x << '\'';}
void __print(const char *x) {cerr << '\"' << x << '\"';}
void __print(const string &x) {cerr << '\"' << x << '\"';}
void __print(bool x) {cerr << (x ? "true" : "false");}

template<typename T, typename V>
void __print(const pair<T, V> &x) {cerr << '{'; __print(x.first); cerr << ','; __print(x.second); cerr << '}';}
template<typename T>
void __print(const T &x) {int f = 0; cerr << '{'; for (auto &i: x) cerr << (f++ ? "," : ""), __print(i); cerr << "}";}
void _print() {cerr << "]\n";}
template <typename T, typename... V>
void _print(T t, V... v) {__print(t); if (sizeof...(v)) cerr << ", "; _print(v...);}
#ifndef ONLINE_JUDGE
#define debug(x...) cerr << "[" << #x << "] = ["; _print(x)
#else
#define debug(x...)
#endif

//#define int ll

typedef long long ll;
typedef unsigned long long ull;
typedef pair<int,int> pii;
typedef vector<int> vi;
typedef vector<ll> vll;
typedef set<int> si;
typedef multiset<int> msi;
typedef long double ld;
typedef cc_hash_table<size_t, bool, hash<size_t>> ht;

const int mod = 1e9 + 7;


// Schreier–Sims algorithm uzywany z : https://github.com/ShahjalalShohag/code-library/blob/main/Miscellaneous/Schreier–Sims%20algorithm.cpp 

vi inv(vi& p){
    vi ret(p.size());
    for (int i = 0; i < (int)p.size(); i++) ret[p[i]] = i;
    return ret;
}
vi operator * (vi& a, vi& b){
    vi ret(a.size());
    for (int i = 0 ; i < (int)a.size(); i++) ret[i] = b[a[i]];
    return ret;
}
// a group contains all subset products of generators
struct Group {
    int n, m;
    vector<vi> lookup;
    vector<vector<vi>> buckets, ibuckets;
    int yo(vi p, bool add_to_group = 1){
        n = buckets.size();
        for (int i = 0; i < n ; i++){
            int res = lookup[i][p[i]];
            if (res == -1 ){
                if (add_to_group){
                    buckets[i].push_back(p);
                    ibuckets[i].push_back(inv(p));
                    lookup[i][p[i]] = buckets[i].size() - 1;
                }
                return i;
            }
            p = p * ibuckets[i][res];
        }
        return -1;
    }
    ll size() {
        ll ret = 1;
        for (int i = 0; i < n; i++) ret *= buckets[i].size();
        return ret;
    }
    bool in_group(vi g) { return yo(g, false) == -1; }
    Group(vector<vi> &gen, int _n){
    n = _n, m = gen.size(); // m permutations of size n, 0 indexed
    lookup.resize(n);
    buckets.resize(n);
    ibuckets.resize(n);
    for (int i = 0; i < n ; i++){
        lookup[i].resize(n);
        fill(lookup[i].begin(), lookup[i].end(), -1);
    }
    vi id(n);
    for (int i = 0; i < n ; i++) id[i] = i;
    for (int i = 0; i < n ; i++){
        buckets[i].push_back(id);
        ibuckets[i].push_back(id);
        lookup[i][i] = 0;
    }
    for (int i = 0; i < m ; i++) yo(gen[i]);
    queue<pair<pair<int, int>,pair<int, int>>> q;
    for (int i = 0; i < n ; i++) {
      for (int j = i; j < n ; j++) {
        for (int k = 0; k < (int)buckets[i].size(); k++) {
          for (int l = 0; l < (int)buckets[j].size(); l++) {
            q.push({pair<int, int>(i, k), pair<int, int>(j, l)});
          }
        }
      }
    }
    while(!q.empty()) {
        pair<int, int> a = q.front().first;
        pair<int, int> b = q.front().second;
        q.pop();
        int res = yo(buckets[a.first][a.second] * buckets[b.first][b.second]);
        if (res == -1) continue;
        pair<int, int> cur(res, (int)buckets[res].size() - 1);
        for (int i = 0; i < n; i ++) {
            for (int j = 0; j < (int)buckets[i].size(); ++j){
            if (i <= res) q.push(make_pair(pair<int, int>(i , j), cur));
            if (res <= i) q.push(make_pair(cur, pair<int, int>(i, j)));
            }
        }
    }
  }
};

// koniec kodu z https://github.com/ShahjalalShohag/code-library/blob/main/Miscellaneous/Schreier–Sims%20algorithm.cpp 

int bin_exp(int a, int b) {
    if (b == 0) {
        return 1;
    }
    if (b % 2) {
        return 1LL * bin_exp(a, b - 1) * a % mod;
    }
    int res = bin_exp(a, b / 2);
    return 1LL * res * res % mod;
}

int Inv(int a) {
    return bin_exp(a, mod - 2);
}

//int inver(vi &a) {
    //int n = sajz(a);
    //int ile = 0;
    //for (int i = 0; i < n; i ++) {
        //for (int j = i + 1; j < n; j ++) {
            //ile += (a[i] > a[j]);
        //}
    //}
    //return ile;
//}

const int MX = (1 << 13);
int pods;

int t[MX*2];

void add(int v, int x) {
	t[v += pods] = x;
	while (v/2) {
		v/=2;
		t[v] = t[v*2] + t[v*2+1];
	}
}

int suma(int l, int r) {
	int res = 0;
	for (l += pods, r += pods; l < r; l >>= 1, r >>= 1) {
		if (l&1) res += t[l++];
		if (r&1) res += t[--r]; 
	}
	return res;
}

int inver(vi &a) {
		
	for (int i = 0; i <= 2*pods; i ++) t[i] = 0;
	
	int n = sajz(a);
	int res = 0;
	for (int i = 0; i < n; i ++) {
		res += suma(a[i]+1, n);
		add(a[i], 1);
	}
	return res;
}


// kod z : https://stackoverflow.com/questions/20511347/a-good-hash-function-for-a-vector

struct Vec {
    vi vec;

    size_t operator()() {
        size_t seed = vec.size();
        for(auto& i : vec) {
            seed ^= i + 0x9e3779b9 + (seed << 6) + (seed >> 2);
        }
        return seed;
    }
};

int32_t main() {
	ios_base::sync_with_stdio(false);
	cout.tie(0);
	cin.tie(0);

    //mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());

    int n, k;
    cin >> n >> k;
		
	pods = 1;
    while (pods <= n) pods*=2;

    if (k == 1) {
		
        Vec a;
        for (int i = 0; i < n; i ++) {
            int x;
            cin >> x;
            x --;
            a.vec.pb(x);
        }
         
        vi b = a.vec;

        ll sum = 0, cnt = 0;

        //map<size_t, bool> M;
        ht M;

        while (!M[a()]) {
            M[a()] = true;
            cnt ++;
            sum += inver(a.vec);
            sum %= mod;
            a.vec = a.vec * b;
        }

        ll up = sum % mod;
        ll down = Inv(cnt) % mod;
        ll ans = (up * down) % mod;
        
        // 625, 721 zamula
        
        //debug(cnt);

        cout << ans << '\n';
    } else {

        vector<vi> base;
        while (k--) {
            vi v;
            for (int i = 0; i < n; i++) {
                int x; cin >> x;
                v.push_back(x - 1);
            }
            base.push_back(v);
        }

        Group g(base, n);

        int Group_size = g.size();
        //debug(Group_size);

        vi perm(n);
        for (int i = 0; i < n; i ++) perm[i] = i;

        ll nom = 0, denom = 0;

        do {
            if (denom == Group_size) break;
            if (g.in_group(perm)) { // jest w grupie
                denom ++;
                nom += inver(perm);
                nom %= mod;
            }
        } while (next_permutation(all(perm)));

        ll ans = (nom * Inv(denom)) % mod;
        cout << ans << '\n';
    }

    return 0;
}