#include <iostream>
#include <queue>
#include <cstdio>
#include <string>
#include <cstring>
using namespace std;
const int SD = 26;
const int MAXL = 1000;
struct Tire {int next[MAXL][SD], fail[MAXL], eofs[MAXL];int Root, cnt;int newnode() {for (int i = 0; i < SD; i++)     next[cnt][i] = -1;eofs[cnt++] = 0;return cnt - 1;}void init() {cnt = 0;Root = newnode();}void Ins (char buf[], int k) {int len = strlen (buf);int now = Root;for (int i = 0; i < len; i++) {if (next[now][buf[i] - 'a'] == -1)next[now][buf[i] - 'a'] = newnode();now = next[now][buf[i] - 'a'];}eofs[now] |= (1 << k);}void build() {queue<int> ql;fail[Root] = Root;for (int i = 0; i < SD; i++) {if (next[Root][i] == -1)next[Root][i] = Root;else {fail[next[Root][i]] = Root;ql.push (next[Root][i]);}}while (!ql.empty() ) {int now = ql.front(); ql.pop();eofs[now] |= eofs[fail[now]];for (int i = 0; i < SD; i++)if (next[now][i] == -1) {next[now][i] = next[fail[now]][i];}else {fail[next[now][i]] = next[fail[now]][i];ql.push (next[now][i]);}}}
} AC;
int Cs, n, m;
char s[20];
double dp[20][400][1 << 9], tmp = 1. / 26;
int main() {scanf ("%d", &Cs);while (Cs--) {memset (dp, 0, sizeof dp);AC.init();scanf ("%d %d", &n, &m);for (int i = 0; i < n; i++) {scanf ("%s", s);AC.Ins (s, i);}AC.build();dp[0][0][0] = 1;for (int i = 0; i < m; i++)for (int u = 0; u < AC.cnt; u++)for (int st = 0; st < (1 << n); st++)if (dp[i][u][st] > 0)for (int j = 0; j < SD; j++) {int v = AC.next[u][j];dp[i + 1][v][st | AC.eofs[v]] += dp[i][u][st] * tmp;}double ans = 0;for (int i = 0; i < AC.cnt; i++)for (int st = 0; st < (1 << n); st++)if (dp[m][i][st] > 0) {int sum = 0;for (int k = 0; k < n; k++)if (st & (1 << k) ) sum++;ans += dp[m][i][st] * sum;}printf ("%.6f\n", ans);}
}