#include <bits/stdc++.h>
using namespace std;
#define FOR(i,m,n) for(int i=(m);i<(n);++i)
#define REP(i,n) FOR(i,0,n)
using ll = long long;
constexpr int INF = 0x3f3f3f3f;
constexpr long long LINF = 0x3f3f3f3f3f3f3f3fLL;
constexpr double EPS = 1e-8;
constexpr int MOD = 998244353;
// constexpr int MOD = 1000000007;
constexpr int DY4[]{1, 0, -1, 0}, DX4[]{0, -1, 0, 1};
constexpr int DY8[]{1, 1, 0, -1, -1, -1, 0, 1};
constexpr int DX8[]{0, -1, -1, -1, 0, 1, 1, 1};
template <typename T, typename U>
inline bool chmax(T& a, U b) { return a < b ? (a = b, true) : false; }
template <typename T, typename U>
inline bool chmin(T& a, U b) { return a > b ? (a = b, true) : false; }
struct IOSetup {
  IOSetup() {
    std::cin.tie(nullptr);
    std::ios_base::sync_with_stdio(false);
    std::cout << fixed << setprecision(20);
  }
} iosetup;

struct Manacher {
  template <typename T>
  explicit Manacher(const T& s) {
    T str;
    int n = s.size();
    str.reserve(n * 2 + 1);
    for (int i = 0; i < n; ++i) {
      str.push_back(s[i]);
      str.push_back('$');
    }
    str.pop_back();
    n = str.size();
    radius.resize(n);
    for (int i = 0, j = 1; i < n;) {
      while (i - j >= 0 && i + j < n && str[i - j] == str[i + j]) ++j;
      radius[i] = j;
      int k = 1;
      for (; i - k >= 0 && i + k < n && k + radius[i - k] < j; ++k) {
        radius[i + k] = radius[i - k];
      }
      i += k;
      j -= k;
    }
  }

  int odd(const int idx) const { return (radius[idx * 2] + 1) / 2; }

  int even(const int idx) const { return radius[idx * 2 + 1] / 2; }

  bool is_palindrome(const int left, const int right) const {
    const int mid = (left + right - 1) / 2;
    return ((right - left) & 1 ? odd(mid) * 2 - 1 : even(mid) * 2)
           >= right - left;
  }

 private:
  std::vector<int> radius;
};

int solve(const int m, string s) {
  const int n = s.length();
  for (int op = 1; op <= 3; ++op) {
    string u = "";
    REP(_, op) u += s;
    const Manacher manacher(u);
    REP(i, n * op) {
      if ((manacher.odd(i) - 1) * 2 + 1 >= m) return op;
    }
    REP(i, n * op - 1) {
      if (manacher.even(i) * 2 >= m) return op;
    }
  }
  if (m * 2 <= n) return -1;
  Manacher manacher(s + s + s);
  int ans = INF;
  REP(i, n) {
    if ((manacher.odd(i + n) - 1) * 2 + 1 >= n) {
      chmin(ans, 1 + (m / 2 - i + n - 1) / n + (m / 2 - (n - 1 - i) + n - 1) / n);
    }
  }
  REP(i, n - 1) {
    if (manacher.even(i + n) * 2 >= n) {
      chmin(ans, 1 + ((m + 1) / 2 - (i + 1) + n - 1) / n + ((m + 1) / 2 - (n - 1 - i) + n - 1) / n);
    }
  }
  if (manacher.is_palindrome(0, n)) chmin(ans, ((m + 1) / 2 + n - 1) / n + ((m + 1) / 2 + n - 1) / n);
  return ans == INF ? -1 : ans;
}

int main() {
  int t; cin >> t;
  while (t--) {
    int n, m; string s; cin >> n >> m >> s;
    cout << solve(m, s) << '\n';
  }
  return 0;
}