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
#include <bits/stdc++.h>
#define fi first
#define sc second
#define pb push_back
#define rep(i,p,k) for(int i=(p);i<(k);++i)
#define forn(i,p,k) for(int i=(p);i<=(k);++i)
#define forr(i,k,p) for(int i=(k)-1;i>=(p);--i)
#define each(a,b) for(auto&a:b)
#define all(v)  begin(v), end(v)
#define RET(smth)   return void(cout<<(smth)<<'\n');
#define sz(v) (int)v.size()
using namespace std;
using pii = pair<int,int>;
using ll = long long;
using Vi = vector<int>;
#ifdef DEBUG
#include "debug.h"
#else
#define debug(...) ;
#endif

const int MM = 3013;
int par[MM*MM];
int L[MM*MM];
int inv[MM*MM];

int find(int x) {
    return par[x] < 0 ? x : par[x] = find(par[x]);
}

void Union(int a, int b) {
    a = find(a);
    b = find(b);
    if(a == b) return;
    if(par[a] > par[b]) swap(a,b);
    par[a] += par[b];
    par[b] = a;
    L[a] += L[b];
}

const int P = 1e9 + 7;

int mul(int a, int b) {
    return 1LL*a*b%P;
}

int main() {
#ifndef DEBUG
    cin.tie(0) -> sync_with_stdio(0);
#endif
    int n,k; cin >> n >> k;
    fill(par,par+n*n,-1);
    inv[1] = 1;
    rep(i,2,n*n + 1) inv[i] = mul(P/i, P - inv[P%i]);
    rep(i,0,n) rep(j,i+1,n) L[i*n+j] = 1;
    Vi T(n);
    while(k--) {
        for(auto&v:T) cin >> v, --v;
        rep(i,0,n) rep(j,0,n) if(i!=j)  Union(i*n+j,T[i]*n+T[j]);
        if(n != 1 && -par[find(1)] == n*(n-1)) break;
    }
    ll res = 0;
    rep(i,0,n) rep(j,0,n) if(i!=j) {
        int ind = i*n+j;
        if(par[ind] < 0) {
            int orb_size = -par[ind];
            res += mul(inv[orb_size],mul(L[ind],orb_size-L[ind]));
        }
    }
    cout << res % P;
    return 0;
}