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#include <bits/stdc++.h>
using namespace std;

#define fwd(i, a, n) for (int i = (a); i < (n); i ++)
#define rep(i, n) fwd(i, 0, n)
#define all(X) begin(X), end(X)
#define sz(X) ((int)X.size())
#define st first
#define nd second
#define pii pair<int, int>
#define vi vector<int>

#ifdef LOC
auto &operator << (auto &out, pair<auto, auto> a) {
	return out << "(" << a.st << ", " << a.nd << ")";
}

auto &operator << (auto &out, auto a) {
	out << "{";
	for (auto b : a)
		out << b << ", ";
	return out << "}";
}

void dump(auto... x) { ((cerr << x << ", "), ...) << '\n'; }

#define debug(x...) cerr << "[" #x "]: ", dump(x)
#else
#define debug(...) 0
#endif

#define my_getchar() (S == T && (T = (S = BB) + fread_unlocked(BB, 1, 1 << 15, stdin), S == T) ? EOF : *S++)
char BB[1 << 20], *S = BB, *T = BB;
inline void read(int &x) {
    x = 0;
    char c = my_getchar();
    while (isdigit(c)) {
        x = 10 * x + (c & 15);
		c = my_getchar();
	}
}

const int B = 12;
const int maxN = 3000;
const int maxV = (maxN << B);

int col[maxV + 1];
vi g[maxV];

int uni_cnt = 0;

void __attribute__ ((noinline)) uni(int v, int u, int who) {
	if (who) {
		uni(v, u, 0);
	} else {
		v = (v >> B) + ((v % (1 << B)) << B);
		u = (u >> B) + ((u % (1 << B)) << B);
	}
	uni_cnt += 1;
	v = col[v];
	u = col[u];
	if (v == u)
		return;
	if (sz(g[v]) < sz(g[u]))
		swap(v, u);
	for (auto w : g[u]) {
		col[w] = v;
		g[v].push_back(w);
	}
	g[u].clear();
	g[u].shrink_to_fit();
}

int pot(int a, int w, int mod) {
	int res = 1;
	while (w) {
		if (w & 1)
			res = 1ll * res * a % mod;
		w /= 2;
		a = 1ll * a * a % mod;
	}
	return res;
}

int32_t main() {
	int n, k;
	read(n);
	read(k);
	int N = n << B;
	iota(col, col + N, 0);
	rep(i, N)
		g[i].push_back(i);
	int p[maxN];
	rep(i, k) {
		rep(j, n) {
			read(p[j]);
			p[j] -= 1;
		}
		for (int a = 0; a < n; a ++) {
			int aB = a << B;
			int pa = p[a];
			int paB = p[a] << B;
			for (int b = a - 4; b >= 0; b -= 4) {
				if (col[aB + b] != col[paB + p[b]]) {
					uni(aB + b, paB + p[b], 1);
				}
				if (col[aB + b + 1] != col[paB + p[b + 1]]) {
					uni(aB + b + 1, paB + p[b + 1], 1);
				}
				if (col[aB + b + 2] != col[paB + p[b + 2]]) {
					uni(aB + b + 2, paB + p[b + 2], 1);
				}
				if (col[aB + b + 3] != col[paB + p[b + 3]]) {
					uni(aB + b + 3, paB + p[b + 3], 1);
				}
			}
			if (a % 4) {
				if (col[aB] != col[paB + p[0]]) {
					uni(aB, paB + p[0], 1);
				}
			}
			if (a % 4 >= 2) {
				if (col[aB + 1] != col[paB + p[1]]) {
					uni(aB + 1, paB + p[1], 1);
				}
			}
			if (a % 4 == 3) {
				if (col[aB + 2] != col[paB + p[2]]) {
					uni(aB + 2, paB + p[2], 1);
				}
			}
		}
	}
	const int mod = 1e9 + 7;
	int ans = 0;
	col[0] = 1;
	fwd(i, 1, N + 1)
		col[i] = 1ll * col[i - 1] * i % mod;
	col[N] = pot(col[N], mod - 2, mod);
	for (int i = N; i; i --) {
		int inv = 1ll * col[i] * col[i - 1] % mod;
		col[i - 1] = 1ll * col[i] * i % mod;
		col[i] = inv;
	}
	rep(i, N) {
		int a = 0;
		int b = 0;
		for (auto v : g[i]) {
			int l = (v >> B);
			int r = v % (1 << B);
			if (l < r) {
				a += 1;
			} else if (l > r) {
				b += 1;
			}
		}
		int cont = (1ll * a * b % mod) * col[a + b] % mod;
		ans = (ans + cont) % mod;
	}
	printf("%d\n", ans);
   	return 0;
}