// #pragma GCC optimize("O3,unroll-loops")
#include <bits/stdc++.h>
// #include <x86intrin.h>
using namespace std;
#if __cplusplus >= 202002L
using namespace numbers;
#endif

template<class data_t, data_t _mod>
struct modular_fixed_base{
#define IS_INTEGRAL(T) (is_integral_v<T> || is_same_v<T, __int128_t> || is_same_v<T, __uint128_t>)
#define IS_UNSIGNED(T) (is_unsigned_v<T> || is_same_v<T, __uint128_t>)
	static_assert(IS_UNSIGNED(data_t));
	static_assert(_mod >= 1);
	static constexpr bool VARIATE_MOD_FLAG = false;
	static constexpr data_t mod(){
		return _mod;
	}
	template<class T>
	static vector<modular_fixed_base> precalc_power(T base, int SZ){
		vector<modular_fixed_base> res(SZ + 1, 1);
		for(auto i = 1; i <= SZ; ++ i) res[i] = res[i - 1] * base;
		return res;
	}	
	static vector<modular_fixed_base> _INV;
	static void precalc_inverse(int SZ){
		if(_INV.empty()) _INV.assign(2, 1);
		for(auto x = _INV.size(); x <= SZ; ++ x) _INV.push_back(_mod / x * -_INV[_mod % x]);
	}
	// _mod must be a prime
	static modular_fixed_base _primitive_root;
	static modular_fixed_base primitive_root(){
		if(_primitive_root) return _primitive_root;
		if(_mod == 2) return _primitive_root = 1;
		if(_mod == 998244353) return _primitive_root = 3;
		data_t divs[20] = {};
		divs[0] = 2;
		int cnt = 1;
		data_t x = (_mod - 1) / 2;
		while(x % 2 == 0) x /= 2;
		for(auto i = 3; 1LL * i * i <= x; i += 2){
			if(x % i == 0){
				divs[cnt ++] = i;
				while(x % i == 0) x /= i;
			}
		}
		if(x > 1) divs[cnt ++] = x;
		for(auto g = 2; ; ++ g){
			bool ok = true;
			for(auto i = 0; i < cnt; ++ i){
				if((modular_fixed_base(g).power((_mod - 1) / divs[i])) == 1){
					ok = false;
					break;
				}
			}
			if(ok) return _primitive_root = g;
		}
	}
	constexpr modular_fixed_base(){ }
	modular_fixed_base(const double &x){ data = _normalize(llround(x)); }
	modular_fixed_base(const long double &x){ data = _normalize(llround(x)); }
	template<class T, typename enable_if<IS_INTEGRAL(T)>::type* = nullptr> modular_fixed_base(const T &x){ data = _normalize(x); }
	template<class T, typename enable_if<IS_INTEGRAL(T)>::type* = nullptr> static data_t _normalize(const T &x){
		int sign = x >= 0 ? 1 : -1;
		data_t v =  _mod <= sign * x ? sign * x % _mod : sign * x;
		if(sign == -1 && v) v = _mod - v;
		return v;
	}
	template<class T, typename enable_if<IS_INTEGRAL(T)>::type* = nullptr> operator T() const{ return data; }
	modular_fixed_base &operator+=(const modular_fixed_base &otr){ if((data += otr.data) >= _mod) data -= _mod; return *this; }
	modular_fixed_base &operator-=(const modular_fixed_base &otr){ if((data += _mod - otr.data) >= _mod) data -= _mod; return *this; }
	template<class T, typename enable_if<IS_INTEGRAL(T)>::type* = nullptr> modular_fixed_base &operator+=(const T &otr){ return *this += modular_fixed_base(otr); }
	template<class T, typename enable_if<IS_INTEGRAL(T)>::type* = nullptr> modular_fixed_base &operator-=(const T &otr){ return *this -= modular_fixed_base(otr); }
	modular_fixed_base &operator++(){ return *this += 1; }
	modular_fixed_base &operator--(){ return *this += _mod - 1; }
	modular_fixed_base operator++(int){ modular_fixed_base result(*this); *this += 1; return result; }
	modular_fixed_base operator--(int){ modular_fixed_base result(*this); *this += _mod - 1; return result; }
	modular_fixed_base operator-() const{ return modular_fixed_base(_mod - data); }
	modular_fixed_base &operator*=(const modular_fixed_base &rhs){
		if constexpr(is_same_v<data_t, unsigned int>) data = (unsigned long long)data * rhs.data % _mod;
		else if constexpr(is_same_v<data_t, unsigned long long>){
			long long res = data * rhs.data - _mod * (unsigned long long)(1.L / _mod * data * rhs.data);
			data = res + _mod * (res < 0) - _mod * (res >= (long long)_mod);
		}
		else data = _normalize(data * rhs.data);
		return *this;
	}
	template<class T, typename enable_if<IS_INTEGRAL(T)>::type* = nullptr>
	modular_fixed_base &inplace_power(T e){
		if(e == 0) return *this = 1;
		if(data == 0) return *this = {};
		if(data == 1) return *this;
		if(data == mod() - 1) return e % 2 ? *this : *this = -*this;
		if(e < 0) *this = 1 / *this, e = -e;
		modular_fixed_base res = 1;
		for(; e; *this *= *this, e >>= 1) if(e & 1) res *= *this;
		return *this = res;
	}
	template<class T, typename enable_if<IS_INTEGRAL(T)>::type* = nullptr>
	modular_fixed_base power(T e) const{
		return modular_fixed_base(*this).inplace_power(e);
	}
	modular_fixed_base &operator/=(const modular_fixed_base &otr){
		make_signed_t<data_t> a = otr.data, m = _mod, u = 0, v = 1;
		if(a < _INV.size()) return *this *= _INV[a];
		while(a){
			make_signed_t<data_t> t = m / a;
			m -= t * a; swap(a, m);
			u -= t * v; swap(u, v);
		}
		assert(m == 1);
		return *this *= u;
	}
#define ARITHMETIC_OP(op, apply_op)\
modular_fixed_base operator op(const modular_fixed_base &x) const{ return modular_fixed_base(*this) apply_op x; }\
template<class T, typename enable_if<IS_INTEGRAL(T)>::type* = nullptr>\
modular_fixed_base operator op(const T &x) const{ return modular_fixed_base(*this) apply_op modular_fixed_base(x); }\
template<class T, typename enable_if<IS_INTEGRAL(T)>::type* = nullptr>\
friend modular_fixed_base operator op(const T &x, const modular_fixed_base &y){ return modular_fixed_base(x) apply_op y; }
	ARITHMETIC_OP(+, +=) ARITHMETIC_OP(-, -=) ARITHMETIC_OP(*, *=) ARITHMETIC_OP(/, /=)
#undef ARITHMETIC_OP
#define COMPARE_OP(op)\
bool operator op(const modular_fixed_base &x) const{ return data op x.data; }\
template<class T, typename enable_if<IS_INTEGRAL(T)>::type* = nullptr>\
bool operator op(const T &x) const{ return data op modular_fixed_base(x).data; }\
template<class T, typename enable_if<IS_INTEGRAL(T)>::type* = nullptr>\
friend bool operator op(const T &x, const modular_fixed_base &y){ return modular_fixed_base(x).data op y.data; }
	COMPARE_OP(==) COMPARE_OP(!=) COMPARE_OP(<) COMPARE_OP(<=) COMPARE_OP(>) COMPARE_OP(>=)
#undef COMPARE_OP
	friend istream &operator>>(istream &in, modular_fixed_base &number){
		long long x;
		in >> x;
		number.data = modular_fixed_base::_normalize(x);
		return in;
	}
#define _SHOW_FRACTION
	friend ostream &operator<<(ostream &out, const modular_fixed_base &number){
		out << number.data;
	#if defined(LOCAL) && defined(_SHOW_FRACTION)
		cerr << "(";
		for(auto d = 1; ; ++ d){
			if((number * d).data <= 1000000){
				cerr << (number * d).data;
				if(d != 1) cerr << "/" << d;
				break;
			}
			else if((-number * d).data <= 1000000){
				cerr << "-" << (-number * d).data;
				if(d != 1) cerr << "/" << d;
				break;
			}
		}
		cerr << ")";
	#endif
		return out;
	}
	data_t data = 0;
#undef _SHOW_FRACTION
#undef IS_INTEGRAL
#undef IS_SIGNED
};
template<class data_t, data_t _mod> vector<modular_fixed_base<data_t, _mod>> modular_fixed_base<data_t, _mod>::_INV;
template<class data_t, data_t _mod> modular_fixed_base<data_t, _mod> modular_fixed_base<data_t, _mod>::_primitive_root;

// const unsigned int mod = (119 << 23) + 1; // 998244353
const unsigned int mod = 1e9 + 7; // 1000000007
// const unsigned int mod = 1e9 + 9; // 1000000009
// const unsigned long long mod = (unsigned long long)1e18 + 9;
using modular = modular_fixed_base<decay_t<decltype(mod)>, mod>;

// O(n * log(n))
template<class T, class Compare = less<>>
long long count_inversions(const vector<T> &a, bool count_equal = false, Compare cmp = less<>()){
	int n = (int)a.size();
	vector<T> cmpr = a;
	sort(cmpr.begin(), cmpr.end(), cmp);
	vector<int> sum(n);
	long long res = 0;
	for(auto i = 0; i < n; ++ i){
		int p = lower_bound(cmpr.begin(), cmpr.end(), a[i], cmp) - cmpr.begin();
		res += i;
		for(auto r = p + !count_equal; r > 0; r -= r & -r) res -= sum[r - 1];
		for(++ p; p <= n; p += p & -p) ++ sum[p - 1];
	}
	return res;
}

// DEBUG BEGIN
#ifdef LOCAL
// DECLARATION BEGIN
template<class L, class R> ostream &operator<<(ostream &out, const pair<L, R> &p);
template<class Tuple, size_t N> struct _tuple_printer;
template<class... Args> ostream &_print_tuple(ostream &out, const tuple<Args...> &t);
template<class ...Args> ostream &operator<<(ostream &out, const tuple<Args...> &t);
template<class T> ostream &operator<<(class enable_if<!is_same<T, string>::value, ostream>::type &out, const T &arr);
ostream &operator<<(ostream &out, const _Bit_reference &bit);
template<size_t SZ> ostream &operator<<(ostream &out, const bitset<SZ> &b);
template<class T, class A, class C>
ostream &operator<<(ostream &out, priority_queue<T, A, C> pq);
// DECLARATION END
template<class L, class R> ostream &operator<<(ostream &out, const pair<L, R> &p){
	return out << "{" << p.first << ", " << p.second << "}";
}
template<class Tuple, size_t N> struct _tuple_printer{
	static ostream &_print(ostream &out, const Tuple &t){ return _tuple_printer<Tuple, N-1>::_print(out, t) << ", " << get<N-1>(t); }
};
template<class Tuple> struct _tuple_printer<Tuple, 1>{
	static ostream &_print(ostream &out, const Tuple& t){ return out << get<0>(t); }
};
template<class... Args> ostream &_print_tuple(ostream &out, const tuple<Args...> &t){
	return _tuple_printer<decltype(t), sizeof...(Args)>::_print(out << "{", t) << "}";
}
template<class ...Args> ostream &operator<<(ostream &out, const tuple<Args...> &t){
	return _print_tuple(out, t);
}
template<class T> ostream &operator<<(class enable_if<!is_same<T, string>::value, ostream>::type &out, const T &arr){
	if(arr.empty()) return out << "{}";
	out << "{";
	for(auto it = arr.begin(); it != arr.end(); ++ it){
		out << *it;
		next(it) != arr.end() ? out << ", " : out << "}";
	}
	return out;
}
ostream &operator<<(ostream &out, const _Bit_reference &bit){
	return out << bool(bit);
}
template<size_t SZ> ostream &operator<<(ostream &out, const bitset<SZ> &b){
	for(auto i = 0; i < SZ; ++ i) out << b[i];
	return out;
}
template<class T, class A, class C>
ostream &operator<<(ostream &out, priority_queue<T, A, C> pq){
	vector<T> a;
	while(!pq.empty()) a.push_back(pq.top()), pq.pop();
	return out << a;
}
template<class Head>
void debug_out(Head H){ cerr << H << endl; }
template<class Head, class... Tail>
void debug_out(Head H, Tail... T){ cerr << H << ", ", debug_out(T...); }
void debug2_out(){ }
template<class Head, class... Tail>
void debug2_out(Head H, Tail... T){ cerr << "\n"; for(auto x: H) cerr << x << ",\n"; debug2_out(T...); }
template<class Width, class Head>
void debugbin_out(Width w, Head H){
	for(auto rep = w; rep; -- rep, H >>= 1) cerr << (H & 1);
	cerr << endl;
}
template<class Width, class Head, class... Tail>
void debugbin_out(Width w, Head H, Tail... T){
	for(auto rep = w; rep; -- rep, H >>= 1) cerr << (H & 1);
	cerr << ", "; debugbin_out(w, T...);
}
enum CODE{ CCRED = 31, CCGREEN = 32, CCYELLOW = 33, CCBLUE = 34, CCDEFAULT = 39 };
#define debug_endl() cerr << endl
#define debug(...) cerr << "\033[" << (int)CODE(CCRED) << "mL" << setw(3) << std::left << __LINE__ << std::right << " [" << #__VA_ARGS__ << "] \033[" << (int)CODE(CCBLUE) << "m", debug_out(__VA_ARGS__), cerr << "\33[" << (int)CODE(CCDEFAULT) << "m"
#define debug2(...) cerr << "\033[" << (int)CODE(CCRED) << "mL" << setw(3) << std::left << __LINE__ << std::right << " [" << #__VA_ARGS__ << "] \033[" << (int)CODE(CCBLUE) << "m", debug2_out(__VA_ARGS__), cerr << "\33[" << (int)CODE(CCDEFAULT) << "m"
#define debugbin(...) cerr << "\033[" << (int)CODE(CCRED) << "mL" << setw(3) << std::left << __LINE__ << std::right << " [" << #__VA_ARGS__ << "] \033[" << (int)CODE(CCBLUE) << "m", debugbin_out(__VA_ARGS__), cerr << "\33[" << (int)CODE(CCDEFAULT) << "m"
#else
#define debug_endl() 42
#define debug(...) 42
#define debug2(...) 42
#define debugbin(...) 42
#endif
// DEBUG END

template<bool Enable_small_to_large = true>
struct disjoint_set{
	int n, _group_count;
	vector<int> p;
	vector<list<int>> group;
	disjoint_set(){ }
	disjoint_set(int n): n(n), _group_count(n), p(n, -1), group(n){ assert(n >= 0);
		for(auto i = 0; i < n; ++ i) group[i] = {i};
	}
	int make_set(){
		p.push_back(-1);
		group.push_back(list<int>{p});
		++ _group_count;
		return n ++;
	}
	int root(int u){
		return p[u] < 0 ? u : p[u] = root(p[u]);
	}
	bool share(int a, int b){
		return root(a) == root(b);
	}
	int size(int u){
		return -p[root(u)];
	}
	bool merge(int u, int v){
		u = root(u), v = root(v);
		if(u == v) return false;
		-- _group_count;
		if constexpr(Enable_small_to_large) if(p[u] > p[v]) swap(u, v);
		p[u] += p[v], p[v] = u;
		group[u].splice(group[u].end(), group[v]);
		return true;
	}
	bool merge(int u, int v, auto act){
		u = root(u), v = root(v);
		if(u == v) return false;
		-- _group_count;
		bool swapped = false;
		if constexpr(Enable_small_to_large) if(p[u] > p[v]) swap(u, v), swapped = true;
		p[u] += p[v], p[v] = u;
		group[u].splice(group[u].end(), group[v]);
		act(u, v, swapped);
		return true;
	}
	int group_count() const{
		return _group_count;
	}
	const list<int> &group_of(int u){
		return group[root(u)];
	}
	vector<vector<int>> group_up(){
		vector<vector<int>> g(n);
		for(auto i = 0; i < n; ++ i) g[root(i)].push_back(i);
		g.erase(remove_if(g.begin(), g.end(), [&](auto &s){ return s.empty(); }), g.end());
		return g;
	}
	void clear(){
		_group_count = n;
		fill(p.begin(), p.end(), -1);
		for(auto i = 0; i < n; ++ i) group[i] = {i};
	}
	friend ostream &operator<<(ostream &out, disjoint_set dsu){
		auto gs = dsu.group_up();
		out << "{";
		if(!gs.empty()) for(auto i = 0; i < (int)gs.size(); ++ i){
			out << "{";
			for(auto j = 0; j < (int)gs[i].size(); ++ j){
				out << gs[i][j];
				if(j + 1 < (int)gs[i].size()) out << ", ";
			}
			out << "}";
			if(i + 1 < (int)gs.size()) out << ", ";
		}
		return out << "}";
	}
};

int main(){
	cin.tie(0)->sync_with_stdio(0);
	cin.exceptions(ios::badbit | ios::failbit);
	modular::precalc_inverse(10'000);
	int n, k;
	cin >> n >> k;
	vector p(k, vector<int>(n));
	disjoint_set dsu(n);
	for(auto i = 0; i < k; ++ i){
		for(auto j = 0; j < n; ++ j){
			cin >> p[i][j], -- p[i][j];
			dsu.merge(j, p[i][j]);
		}
	}
	auto groups = dsu.group_up();
	vector<int> is_cyclic((int)groups.size());
	vector<vector<int>> cycle_gen((int)groups.size());
	vector<vector<int>> compress((int)groups.size(), vector<int>(n));
	vector<vector<int>> cycle_pos((int)groups.size(), vector<int>(n));
	modular res = 0;
	for(auto gi = 0; gi < (int)groups.size(); ++ gi){
		const auto &g = groups[gi];
		int m = (int)g.size();
		debug(g);
		for(auto id = 0; id < m; ++ id){
			compress[gi][g[id]] = id;
		}
		static vector<vector<int>> cur;
		cur.assign(k, vector<int>(m));
		for(auto i = 0; i < k; ++ i){
			for(auto id = 0; id < m; ++ id){
				cur[i][id] = compress[gi][p[i][g[id]]];
			}
		}
		debug2(cur);
		int base = -1;
		for(auto i = 0; i < (int)cur.size(); ++ i){
			static vector<int> vis;
			vis.assign(m, false);
			for(auto rep = (int)g.size(), j = 0; rep; -- rep){
				vis[j] = true;
				j = cur[i][j];
			}
			if(ranges::all_of(vis, identity())){
				base = i;
				break;
			}
		}
		debug(base);
		if(~base){
			static vector<vector<int>> gen;
			gen = {vector<int>(m)};
			iota(gen[0].begin(), gen[0].end(), 0);
			for(auto rep = m - 1; rep; -- rep){
				static vector<int> a;
				a.assign(m, -1);
				for(auto j = 0; j < m; ++ j){
					a[j] = gen.back()[cur[base][j]];
				}
				gen.push_back(a);
			}
			ranges::sort(gen);
			debug2(gen);
			for(auto a: cur){
				if(!ranges::binary_search(gen, a)){
					goto FAIL;
				}
			}
			{
				is_cyclic[gi] = true;
				for(auto rep = m, j = g[0]; rep; -- rep){
					cycle_pos[gi][j] = (int)cycle_gen[gi].size();
					cycle_gen[gi].push_back(j);
					j = p[base][j];
				}
				modular sum = 0;
				for(auto a: gen){
					sum += modular(count_inversions(a));
				}
				debug("normal sum", sum);
				res += sum / m;
			}
			debug_endl();
			continue;
		}
		FAIL:;
		debug("failed");
		res += modular(m) * (m - 1) / 4;
		debug_endl();
	}
	debug2(groups);
	debug(res);
	debug(is_cyclic);
	debug2(cycle_gen);
	debug_endl();
	for(auto gi = 0; gi < (int)groups.size(); ++ gi){
		const auto &g = groups[gi];
		for(auto gj = gi + 1; gj < (int)groups.size(); ++ gj){
			const auto &h = groups[gj];
			if(!is_cyclic[gi] || !is_cyclic[gj]){
				array<int, 2> cnt{};
				for(auto j0: g){
					for(auto j1: h){
						++ cnt[j0 < j1];
					}
				}
				modular ratio = modular(cnt[0]) / (cnt[0] + cnt[1]);
				res += modular(cnt[0]) * (1 - ratio) + modular(cnt[1]) * ratio;
				continue;
			}
			int length = gcd((int)g.size(), (int)h.size());
			for(auto i = 0; i < k; ++ i){
				length = gcd(length, abs(cycle_pos[gi][p[i][g[0]]] - cycle_pos[gj][p[i][h[0]]]));
			}
			debug(length);
			vector<array<int, 2>> cnt_index(length), cnt_value(length);
			for(auto li = 0; li < length; ++ li){
				for(auto lj = 0; lj < length; ++ lj){
					int update = (li - lj + length) % length;
					for(auto s = li; s < (int)cycle_gen[gi].size(); s += length){
						int ns = s == (int)cycle_gen[gi].size() - 1 ? 0 : s + 1;
						for(auto t = lj; t < (int)cycle_gen[gj].size(); t += length){
							int nt = t == (int)cycle_gen[gj].size() - 1 ? 0 : t + 1;
							++ cnt_index[update][cycle_gen[gi][s] < cycle_gen[gj][t]];
							++ cnt_value[update][cycle_gen[gi][ns] < cycle_gen[gj][nt]];
						}
					}
				}
			}
			debug(cnt_index);
			debug(cnt_value);
			for(auto dif = 0; dif < length; ++ dif){
				modular ratio = modular(cnt_value[dif][0]) / (cnt_value[dif][0] + cnt_value[dif][1]);
				res += modular(cnt_index[dif][0]) * (1 - ratio) + modular(cnt_index[dif][1]) * ratio;
			}
		}
	}
	cout << res << "\n";
	return 0;
}

/*

*/