#include<bits/stdc++.h>
namespace {
#pragma GCC diagnostic ignored "-Wunused-function"
#include<atcoder/all>
#pragma GCC diagnostic warning "-Wunused-function"
using namespace std;
using namespace atcoder;
#define rep(i,n) for(int i = 0; i < (int)(n); i++)
#define rrep(i,n) for(int i = (int)(n) - 1; i >= 0; i--)
#define all(x) begin(x), end(x)
#define rall(x) rbegin(x), rend(x)
template<class T> bool chmax(T& a, const T& b) { if (a < b) { a = b; return true; } else return false; }
template<class T> bool chmin(T& a, const T& b) { if (b < a) { a = b; return true; } else return false; }
using ll = long long;
using P = pair<int,int>;
using VI = vector<int>;
using VVI = vector<VI>;
using VL = vector<ll>;
using VVL = vector<VL>;

template <class T>
vector<int> Manacher(const T& s) {
  const int n = s.size();
  vector<int> res(n);
  for (int i = 0, r = 1; i < n;) {
    int l = 2 * i - r;
    while (0 <= l && r < n && s[l] == s[r]) l--, r++;
    res[i] = r - i;
    if (++i != r) {
      int j = i - 2;
      while (i + res[j] < r) res[i++] = res[j--];
    }
  }
  return res;
}

template <class T>
vector<int> Manacher_cursor(const T& s) {
  const int n = s.size();
  vector<int> res(n + 1);
  for (int i = 1, r = 1; i < n;) {
    int l = 2 * i - r;
    while (l && r < n && s[l - 1] == s[r]) l--, r++;
    res[i] = r - i;
    if (i++ != r) {
      int j = i - 2;
      while (i + res[j] < r) res[i++] = res[j--];
    } else {
      r = i;
    }
  }
  return res;
}


auto floor_div(signed_integral auto x, signed_integral auto y) {
  return x / y - ((x ^ y) < 0 && x % y != 0);
}
template <integral T>
T floor_div(T x, unsigned_integral auto y) {
  return x >= 0 ? T(x / y) : -T(-x / y + (-x % y != 0));
}
auto ceil_div(signed_integral auto x, signed_integral auto y) {
  return x / y + ((x ^ y) >= 0 && x % y != 0);
}
template <integral T>
T ceil_div(T x, unsigned_integral auto y) {
  return x >= 0 ? T(x / y + (x % y != 0)) : -T(-x / y);
}

} int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  int tt;
  cin >> tt;
  while (tt--) {
    int n, m;
    string s;
    cin >> n >> m >> s;
    s = s + s + s;
    constexpr int INF = 1001001001;
    int ans = INF;
    {
      auto mc = Manacher_cursor(s);
      rep(c, 3 * n + 1) {
        if (mc[c] >= n || 2 * mc[c] >= m) {
          int l = c - (m + 1) / 2, r = c + (m + 1) / 2;
          chmin(ans, floor_div(r - 1, n) - floor_div(l, n) + 1);
        }
      }
    }
    {
      auto me = Manacher(s);
      rep(c, 3 * n) {
        if (me[c] >= n || 2 * me[c] - 1 >= m) {
          int l = c - m / 2, r = c + m / 2;
          chmin(ans, floor_div(r, n) - floor_div(l, n) + 1);
        }
      }
    }
    if (ans == INF) ans = -1;
    cout << ans << '\n';
  }
}