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
#include <bits/stdc++.h>

#pragma GCC optimize("Ofast","unroll-loops")

using namespace std;

#ifdef LOCAL
#include "debug.h"
#else
#define debug(...)
#endif

#define x first
#define y second
#define ir(a, x, b) ((a) <= (x) && (x) <= (b))
#define vec vector
#define rep(i, a, b) for (int i = a; i < (b); ++i)
#define all(x) (x).begin(), (x).end()

using ll = long long;

const ll MOD = ll(1e9)+7;

struct mint {
  int value;

  mint(long long v = 0) { value = v % MOD; if (value < 0) value += MOD;}
  mint(long long a, long long b) : value(0){ *this += a; *this /= b;}

  mint& operator+=(mint const& b) {value += b.value; if (value >= MOD) value -= MOD; return *this;}
  mint& operator-=(mint const& b) {value -= b.value; if (value < 0) value += MOD;return *this;}
  mint& operator*=(mint const& b) {value = (long long)value * b.value % MOD;return *this;}

  friend mint mexp(mint a, long long e) {
    mint res = 1; while (e) { if (e&1) res *= a; a *= a; e >>= 1; }
    return res;
  }
  friend mint inverse(mint a) { return mexp(a, MOD - 2); }

  mint& operator/=(mint const& b) { return *this *= inverse(b); }
  friend mint operator+(mint a, mint const b) { return a += b; }
  friend mint operator-(mint a, mint const b) { return a -= b; }
  friend mint operator-(mint const a) { return 0 - a; }
  friend mint operator*(mint a, mint const b) { return a *= b; }
  friend mint operator/(mint a, mint const b) { return a /= b; }
  friend std::ostream& operator<<(std::ostream& os, mint const& a) {return os << a.value;}
  friend bool operator==(mint const& a, mint const& b) {return a.value == b.value;}
  friend bool operator!=(mint const& a, mint const& b) {return a.value != b.value;}
};

// mint modpow(mint a, mint b) {
//     mint res = 1;
//     while (b) {
//         if (b % 2 == 1) {
//             res *= a;
//         }
//         b /= 2, a *= a;
//     }
//     return res;
// }
//
int n, k;
int e(int i, int j) {
    return n*i + j;
}

const int N = 3000;
int over[N*N];
int tag[N*N];
int find(int x) {
    if (over[x] < 0) {
        return x;
    }
    return over[x] = find(over[x]);
}

    
void unify(int x, int y) {
    // if (over[x] == over[y] && over[x] > 0) return;
    if (over[x] > 0 && over[x] == over[y]) return;
    if (over[x] == y || over[y] == x) return;
    // debug(x, y);
    if ((x = find(x)) == (y = find(y))) return;
    if (over[x] > over[y]) swap(x, y);
    over[x] += over[y];
    over[y] = x;
    tag[x] += tag[y];
}

// int read() {
//     char c;
//     bool b = 0;
//     int n = 0;
//     for (; !ir('0', c, '9'); c = getchar()) {}
//     for (; !ir('0', c, '9'); c = getchar()) {
//         n = 10*n + (c-'0');
//     }
//     return n;
// }
//
int main() {
    ios::sync_with_stdio(0); cin.tie(0); cout.tie(0);
    cin >> n >> k;
    rep (i, 0, n*n) over[i] = -1;
    rep (j, 0, n) {
        rep (i, 0, j) {
            tag[e(i, j)] = 1;
        }
    }
    // printf("type ");
    rep (_, 0, k) {
        // debug(_);
        vec<int> perm(n);
        rep (i, 0, n) {
            cin >> perm[i]; --perm[i];
        }
        rep (i, 0, n) {
            int v = n*i-1;
            rep (j, 0, n) {
                ++v;
                if (i == j) continue;
                unify(v, e(perm[i], perm[j]));
            }
        }
    }
    vec<bool> vis(n*n);
    mint res = n*(n-1)/2;
    rep (i, 0, n) {
        rep (j, 0, n) {
            if (i == j) continue;
            int x = find(e(i, j));
            if (vis[x]) continue;
            vis[x] = true;
            mint tag_ = tag[x], sz_ = -over[x];
            res -= tag_ * tag_ / sz_;
        }
    }
    cout << res << "\n";
    return 0;
}