#include <bits/stdc++.h>
using namespace std;

vector<int> Mana(string &s){ //Manacher
    int n = s.size();
    vector<int> ret(n);
    for(int i=0,w=0; i<n;){
        while(i+w < n && i-w >= 0 && s.at(i-w) == s.at(i+w)) w++;
        ret.at(i) = w;
        int k = 1;
        while(i-k >= 0 && k+ret.at(i-k) < w) ret.at(i+k) = ret.at(i-k),k++;
        i += k; w -= k;
    }  
    return ret;
}
vector<int> Mana2(string s){ //偶数長検出用.
    string t = "";
    for(auto &c : s) t += c,t += '$';
    t.pop_back();
    vector<int> ret = Mana(t); //M[i%2 == 0]=偶数は-1,M[i%2 == 1]=奇数は-1.
    for(int i=0; i<ret.size(); i++) if(i%2 == ret.at(i)%2) ret.at(i)--;
    return ret;
}

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

    int T; cin >> T;
    while(T--){
        int N,M; cin >> N >> M;
        string t; cin >> t;
        string s;
        int answer = -1;
        for(int i=0; i<3; i++){
            s += t;
            auto Ma = Mana2(s);
            for(auto &m : Ma) if(m >= M) answer = i+1;
            if(answer != -1) break;
        }
        if(answer != -1){cout << answer << endl; continue;}
        
        s += t;
        auto Ma = Mana2(s);
        for(int i=0; i<2*N; i++) if(Ma.at(i)+N == Ma.at(i+N)){
            int m = Ma.at(i),m2 = m;
            if(i%2) m2--,i--;
            int left = (M-m+N-1)/N;
            answer = (i/2-((m2+1)/2-1)+1)+m-1+left*N;
            answer = (answer+N-1)/N;
            break;
        }
        cout << answer << "\n";
    }
}