#include <bits/stdc++.h>

using ll = std::int64_t;
using T = std::tuple<int, int, int>;

template <typename C>
std::vector<int> manacher(C seq){
    auto n = seq.size();
    std::vector<int> res(n, 0);
    int c = 0;
    for(int i = 0; i < n; i += 1){
        int ri = c - (i - c);
        if(ri >= 0 && i + res[ri] < c + res[c]){
            res[i] = res[ri];
        }else{
            int j = c + res[c] - i;
            while(i - j >= 0 && i + j < n && seq[i - j] == seq[i + j]){
                j += 1;
            }
            res[i] = j;
            c = i;
        }
    }
    return res;
}

int main(){
    std::cin.tie(nullptr);
    std::ios::sync_with_stdio(false);

    int T;
    std::cin >> T;

    for(int _=0;_<T;_++){
        int N, M;
        std::cin >> N >> M;

        std::string S1;
        std::cin >> S1;
        S1 = S1 + S1 + S1;

        std::string S2(S1.size() * 2, '$');
        for(int i=0;i<S1.size();i++){
            S2[i * 2] = S1[i];
        }

        auto L1 = manacher(S1);
        auto L2 = manacher(S2);

        auto check = [&](int x){
            {
                int last = std::min(x, 2) * N;
                for(int i=0;i<last;i++){
                    int r1 = std::min(L1[i], last - i);
                    int r2 = std::min(L2[i * 2 + 1] / 2, last - (i + 1));
                    int c = std::max(r1 * 2 - 1, r2 * 2);
                    if(c >= M){return true;}
                }
            }

            if(x <= 2){return false;}

            for(int i=N;i<2*N;i++){
                if(L1[i] >= std::max(i - (N - 1), 2 * N - i)){
                    int r = std::min(2 * N - i, i - (N - 1));
                    ll c = 1ll * (1 + (x - 1) / 2 * 2) * (2 * r - 1) + 1ll * (x / 2 * 2) * (N - (2 * r - 1));
                    if(c >= M){
                        return true;
                    }
                }
            }

            for(int i=N;i<2*N;i++){
                int r = L2[i * 2 + 1] / 2;
                if(r >= std::max(i - (N - 1), 2 * N - (i + 1))){
                    int r2 = std::min(2 * N - (i + 1), i - (N - 1));
                    ll c = 1ll * (1 + (x - 1) / 2 * 2) * (2 * r2) + 1ll * (x / 2 * 2) * (N - (2 * r2));
                    if(c >= M){
                        return true;
                    }
                }
            }

            int r = L2[(2 * N - 1) * 2 + 1] / 2;
            if(r >= N){
                ll c = 1ll * (x / 2) * (2 * N);
                if(c >= M){
                    return true;
                }
            }

            return false;
        };

        if(check(2'000'000'000)){
            int ok = 2'000'000'000, ng = 0;
            while(ok - ng >= 2){
                int m = ng + (ok - ng) / 2;
                if(check(m)){
                    ok = m;
                }else{
                    ng = m;
                }
            }
            std::cout << ok << std::endl;
        }else{
            std::cout << -1 << std::endl;
        }
    }
}