#include <algorithm>
#include <atcoder/all>
#include <bitset>
#include <cassert>
#include <cmath>
#include <ctime>
#include <functional>
#include <iomanip>
#include <iostream>
#include <map>
#include <queue>
#include <random>
#include <set>
#include <stack>
#include <string>
#include <tuple>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>
using namespace std;
using namespace atcoder;
typedef long long ll;
#define rep(i, n) for (int i = 0; i < (int)(n); i++)
#define repr(i, n) for (int i = (int)(n) - 1; i >= 0; i--)
#define repk(i, k, n) for (int i = k; i < (int)(n); i++)
#define all(v) v.begin(), v.end()
#define mod1 1000000007
#define mod2 998244353
#define mod3 100000007
#define vi vector<int>
#define vs vector<string>
#define vc vector<char>
#define vl vector<ll>
#define vb vector<bool>
#define vvi vector<vector<int>>
#define vvc vector<vector<char>>
#define vvl vector<vector<ll>>
#define vvb vector<vector<bool>>
#define vvvi vector<vector<vector<int>>>
#define vvvl vector<vector<vector<ll>>>
#define pii pair<int, int>
#define pil pair<int, ll>
#define pli pair<ll, int>
#define pll pair<ll, ll>
#define vpii vector<pair<int, int>>
#define vpll vector<pair<ll, ll>>
#define vvpii vector<vector<pair<int, int>>>
#define vvpll vector<vector<pair<ll, ll>>>

template <typename T>
void debug(T e) {
    cerr << e << endl;
}

template <typename T>
void debug(vector<T> &v) {
    rep(i, v.size()) { cerr << v[i] << " "; }
    cerr << endl;
}

template <typename T>
void debug(vector<vector<T>> &v) {
    rep(i, v.size()) {
        rep(j, v[i].size()) { cerr << v[i][j] << " "; }
        cerr << endl;
    }
}

template <typename T>
void debug(vector<pair<T, T>> &v) {
    rep(i, v.size()) { cerr << v[i].first << " " << v[i].second << endl; }
}

template <typename T>
void debug(set<T> &st) {
    for (auto itr = st.begin(); itr != st.end(); itr++) {
        cerr << *itr << " ";
    }
    cerr << endl;
}

template <typename T>
void debug(multiset<T> &ms) {
    for (auto itr = ms.begin(); itr != ms.end(); itr++) {
        cerr << *itr << " ";
    }
    cerr << endl;
}

template <typename T>
void debug(map<T, T> &mp) {
    for (auto itr = mp.begin(); itr != mp.end(); itr++) {
        cerr << itr->first << " " << itr->second << endl;
    }
}

void debug_out() { cerr << endl; }

template <typename Head, typename... Tail>
void debug_out(Head H, Tail... T) {
    cerr << H << " ";
    debug_out(T...);
}

using mint = modint998244353;

void debug_mint1(vector<mint> &vec) {
    for (int i = 0; i < vec.size(); i++) {
        cerr << vec[i].val() << " ";
    }
    cerr << endl;
}

void debug_mint2(vector<vector<mint>> &vec) {
    for (int i = 0; i < vec.size(); i++) {
        for (int j = 0; j < vec[i].size(); j++) {
            cerr << vec[i][j].val() << " ";
        }
        cerr << endl;
    }
}

vector<ll> manacher(vector<ll> &S){
    const ll ID = 7000000000000000023LL;
    ll N = S.size();
    vector<ll> rad(2 * N - 1, 0);
    vector<ll> T;
    for (ll i = 0; i < N; i++){
        T.push_back(S[i]);
        if (i < N - 1){
            T.push_back(ID);
        }
    }

    ll di = 0;
    ll dj = 0;
    while (di < 2 * N - 1){
        while (dj <= di && di < 2 * N - 1 - dj && T[di - dj] == T[di + dj]){
            dj++;
        }
        rad[di] = dj;
        ll dk = 1;
        while (di >= dk && di < 2 * N - 1 - dk && dj - rad[di - dk] > dk){
            rad[di + dk] = rad[di - dk];
            dk++;
        }
        di += dk;
        dj -= dk;
    }
    for (ll i = 0; i < 2 * N - 1; i++){
        if (i % 2 == rad[i] % 2){
            rad[i]--;
        }
    }
    return rad;
}

int main() {
    ll T;
    cin >> T;
    while (T--){
        ll N, M;
        cin >> N >> M;
        string S;
        cin >> S;
        
        vector<ll> T(0);
        for (ll i = 0; i < 5; i++){
            for (ll j = 0; j < N; j++){
                T.push_back((ll)(S[j] - 'a'));
            }
        }

        ll INF = 10000000000000023LL;

        vector<ll> rad = manacher(T);
        ll ans = INF;
        for (ll i = 4 * N; i < 6 * N; i++){
            // 回文半径が 2N 以上であるなら、必ずできはする
            bool pos = false;
            if (rad[i] >= M){
                pos = true;
            }
            else if (rad[i] >= 2 * N){
                pos = true;
            }
            if (pos){
                if (i % 2 == 0){
                    ll half = M / 2;
                    ll id = (i - 4 * N) / 2;
                    ll left = (id + N - half % N) % N;
                    ll right = (id + half) % N;
                    if (left > right){
                        ans = min(ans, (M + N - 1) / N + 1);
                    }
                    else{
                        ans = min(ans, (M + N - 1) / N);
                    }
                }
                else{
                    ll half = M / 2;
                    ll idl = (i - 4 * N) / 2;
                    ll idr = idl + 1;
                    ll left = (idl + N - half % N) % N;
                    ll right = (idr + half) % N;
                    if (left > right){
                        ans = min(ans, (M + N - 1) / N + 1);
                    }
                    else{
                        ans = min(ans, (M + N - 1) / N);
                    }
                }
            }
        }
        cout << (ans == INF ? -1 : ans) << endl;
    }
}