#include <iostream>
#include <vector>
#include <algorithm>

using namespace std;

vector<int> kai(string &s)
{
  int n = s.size(), c = 0;
  vector<int> ret(n);
  for (int i = 0; i < n; ++i)
  {
    int l = 2 * c - i;
    if (c + ret[c] > i + ret[l]) ret[i] = ret[l];
    else
    {
      int j = max(c + ret[c] - i, 0);
      while (i - j >= 0 && i + j < n && s[i - j] == s[i + j]) ++j;
      ret[i] = j;
      c = i;
    }
  }
  return ret;
}

void solve()
{
  int n, m;
  cin >> n >> m;
  string s;
  cin >> s;
  string tmp(2 * n, '#');
  for (int i = 0; i < n; ++i) tmp[2 * i] = s[i];
  string st = "#";
  int a[5] = {-1, -1, -1, -1, -1};
  for (int i = 0; i < 5; ++i)
  {
    st += tmp;
    auto res = kai(st);
    int val = -1;
    for (auto v : res) val = max(val, v - 1);
    a[i] = val;
  }
  for (int i = 0; i < 5; ++i)
  {
    if (a[i] >= m)
    {
      cout << i + 1 << endl;
      return;
    }
  }
  int d = a[4] - a[3];
  if (d == 0)
  {
    cout << -1 << endl;
    return;
  }
  int ans = (m - a[3] + d - 1) / d + 4;
  cout << ans << endl;
}

int main()
{
  int t;
  cin >> t;
  while (t--) solve();
}