1
  2
  3
  4
  5
  6
  7
  8
  9
 10
 11
 12
 13
 14
 15
 16
 17
 18
 19
 20
 21
 22
 23
 24
 25
 26
 27
 28
 29
 30
 31
 32
 33
 34
 35
 36
 37
 38
 39
 40
 41
 42
 43
 44
 45
 46
 47
 48
 49
 50
 51
 52
 53
 54
 55
 56
 57
 58
 59
 60
 61
 62
 63
 64
 65
 66
 67
 68
 69
 70
 71
 72
 73
 74
 75
 76
 77
 78
 79
 80
 81
 82
 83
 84
 85
 86
 87
 88
 89
 90
 91
 92
 93
 94
 95
 96
 97
 98
 99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
#include<bits/stdc++.h>
 
//#pragma GCC optimize("Ofast")
//#pragma GCC optimize("trapv")
 
#define st first
#define nd second
#define pb push_back
#define pp pop_back
#define eb emplace_back
#define mp(a, b) make_pair(a, b)
#define all(x) (x).begin(), (x).end()
#define rev(x) reverse(all(x))
#define sor(x) sort(all(x))
#define sz(x) (int)(x).size()
#define rsz(x) resize(x)
 
using namespace std;
 
///~~~~~~~~~~~~~~~~~~~~~~~~~~
 
template <typename H, typename T> 
ostream& operator<<(ostream& os, pair<H, T> m){
	return os <<"("<< m.st<<", "<<m.nd<<")";
}
template <typename H> 
ostream& operator<<(ostream& os, vector<H> V){
	os<<"{";
	for(int i=0; i<V.size(); i++){
		if(i)os<<" ";
		os<<V[i];
	}
	os<<"}";
	return os;
}
 
void debug(){cerr<<"\n";}
template <typename H, typename... T>
void debug(H h, T... t) {cerr<<h; if (sizeof...(t)) cerr << ", "; debug(t...);}
#define deb(x...) cerr<<#x<<" = ";debug(x);
 
///~~~~~~~~~~~~~~~~~~~~~~~~~
 
typedef long long ll;
typedef long double ld;
typedef pair<int, int> pii;
typedef pair<ll, ll> pll;
typedef vector<int> vi;
typedef vector<pii > vii;
typedef vector<ll> vl;
typedef vector<pll> vll;
typedef string str;
 
#define BOOST ios_base::sync_with_stdio(false);cin.tie(NULL);cout.tie(NULL);
 
mt19937 rng(chrono::high_resolution_clock::now().time_since_epoch().count());
 
const int N=3e3+5, INF=1e9+5, mod=1e9+7;

struct modint{
	int n=0;
	modint(){}
	modint(ll x){
		n=x%mod;
		if(n<0)n+=mod;
	}
	operator int(){
		return n;
	}
	modint operator+(modint a){a.n = n+a.n; if(a.n>=mod)a.n-=mod;return a;}
	modint operator+=(modint a){return (*this)=(*this)+a;}
	modint operator-(modint a){a.n = n-a.n; if(a.n<0)a.n+=mod;return a;}
	modint operator-=(modint a){return (*this)=(*this)-a;}
	modint operator*(modint a){a.n = (n*1ll*a.n)%mod; return a;}
	modint operator*=(modint a){return (*this)=(*this)*a;}
	modint por(const ll &m)const{
		modint a(1);
		if(m==0)return a;
		if(m==1)return (*this);
		a=por(m/2);
		a*=a;
		return a*(por(m&1));
	}
	modint odw(){
		return por((ll)mod-2);
	}
	modint operator/(modint a){return (*this)*a.odw();}
	modint operator/=(modint a){return (*this)=(*this)/a;}
	bool operator==(modint a){return a.n==n;}
	friend ostream& operator<<(ostream& os, modint m) {
		return os << m.n; 
	}
};

int num[N][N];
int r[N*N], dobre[N*N], zle[N*N];
int find(int v){
	if(v==r[v]){
		return v;
	}
	return r[v]=find(r[v]);
}
void zloz(vi &p, vi &q){
	//deb(q);
	for(int &i:q){
		i=p[i];
	}
	//deb(q);
}

int main(){
	BOOST;
	int n, k;
	cin>>n>>k;
	//n=3000;k=3000;
	vector V(k, vi(n));
	for(int i=0; i<k; i++){
		for(int &j:V[i])cin>>j, j--;
		//iota(all(V[i]), 0);
		//shuffle(all(V[i]), rng);
	}
	for(int i=0; i<n; i++){
		for(int j=0; j<n; j++){
			num[i][j]=i*n+j;
			r[i*n+j]=i*n+j;
		}
	}
	int prob=150;//Uwaga: jeśli n<=1000 nalezy testowac wszystkie zbiory
	if(n<=3000){
		prob*=3000/n;
		prob*=3000/n;
		prob=min(prob, k);
	}
	for(int ii=0; ii<prob; ii++){
		vector<int> V2(n);
		if(prob==k){
			V2=V[ii];
		}
		else{
			iota(all(V2), 0);
			int t=n+n+rng()%n;
			for(int jj=0; jj<t; jj++){
				zloz(V[rng()%k], V2);
			}
		}
		for(int i=0; i<n; i++){
			for(int j=0; j<n; j++){
				if(i==j)continue;
				int a=find(n*i+j), b=find(n*V2[i]+V2[j]);
				//deb(i, j, V[ii][i], V[ii][j]);
				if(a!=b){
					r[a]=b;
				}
			}
		}
	}
	for(int i=0; i<n; i++){
		for(int j=0; j<n; j++){
			if(i<j){
				dobre[find(n*i+j)]++;
			}
			else zle[find(n*i+j)]++;
		}
	}
	modint ans(0);
	for(int i=0; i<n; i++){
		for(int j=0; j<n; j++){
			int t=i*n+j;
			if(i!=j && r[t]==t){
				//deb(i, j, dobre[t], zle[t]);
				ans+=modint(dobre[t])*modint(zle[t])/(modint(dobre[t]+zle[t]));
			}
		}
	}
	cout<<ans<<"\n";
}