#include <bits/stdc++.h>
using namespace std;
using std::cout;
using std::cin;
using std::endl;
using ll=long long;
using ld=long double;
const ll ILL=2167167167167167167;
const int INF=2100000000;
const int mod=998244353;
#define rep(i,a,b) for (int i=(int)(a);i<(int)(b);i++)
#define all(p) p.begin(),p.end()
template<class T> using _pq = priority_queue<T, vector<T>, greater<T>>;
template<class T> ll LB(vector<T> &v,T a){return lower_bound(v.begin(),v.end(),a)-v.begin();}
template<class T> ll UB(vector<T> &v,T a){return upper_bound(v.begin(),v.end(),a)-v.begin();}
template<class T> bool chmin(T &a,T b){if(a>b){a=b;return 1;}else return 0;}
template<class T> bool chmax(T &a,T b){if(a<b){a=b;return 1;}else return 0;}
template<class T> void So(vector<T> &v) {sort(v.begin(),v.end());}
template<class T> void Sore(vector<T> &v) {sort(v.begin(),v.end(),[](T x,T y){return x>y;});}
bool yneos(bool a,bool upp=0){if(a){cout<<(upp?"YES\n":"Yes\n");}else{cout<<(upp?"NO\n":"No\n");}return a;}
template<class T> void vec_out(vector<T> &p,int ty=0){
if(ty==2){cout<<'{';for(int i=0;i<(int)p.size();i++){if(i){cout<<",";}cout<<'"'<<p[i]<<'"';}cout<<"}\n";}
else{if(ty==1){cout<<p.size()<<"\n";}for(int i=0;i<(int)(p.size());i++){if(i) cout<<" ";cout<<p[i];}cout<<"\n";}}
template<class T> T vec_min(vector<T> &a){assert(!a.empty());T ans=a[0];for(auto &x:a) chmin(ans,x);return ans;}
template<class T> T vec_max(vector<T> &a){assert(!a.empty());T ans=a[0];for(auto &x:a) chmax(ans,x);return ans;}
template<class T> T vec_sum(vector<T> &a){T ans=T(0);for(auto &x:a) ans+=x;return ans;}
int pop_count(long long a){int res=0;while(a){res+=(a&1),a>>=1;}return res;}
template<class T> bool inside(T l,T x,T r){return l<=x&&x<r;}

using u64 = uint64_t;
struct RollingHash {
    static inline const u64 mod = 0x1FFF'FFFF'FFFF'FFFF, base = mt19937_64{random_device{}()}() % mod;
    ll n;
    vector<u64> hash, pow;
    static u64 add(u64 a, u64 b) {
        a += b;
        if(a >= mod) a -= mod;
        return a;
    }
    static u64 mul(u64 a, u64 b) {
        auto c = __uint128_t(a) * b;
        return add(c >> 61, c & mod);
    }
    RollingHash(const string& s): n(s.size()), hash(n + 1), pow(n + 1, 1) {
        for(ll i = 0; i < n; i++) {
            pow[i + 1] = mul(pow[i], base);
            hash[i + 1] = add(mul(hash[i], base), s[i]);
        }
    }
    u64 get(ll l, ll r) const {
        return add(hash[r], mod - mul(hash[l], pow[r - l]));
    }
};

void solve();
// CYAN / FREDERIC
int main() {
    ios::sync_with_stdio(false);
    cin.tie(nullptr);
    
    int t = 1;
    cin >> t;
    rep(i, 0, t) solve();
}

void solve(){
    ll N, M;
    cin >> N >> M;
    string S;
    cin >> S;
    auto f = [&]() -> vector<u64> {
        RollingHash H(S);
        vector<u64> res(N);
        using F = pair<u64, u64>;
        F a = {H.get(0, N), H.pow[N]};
        auto mul = [&](F l, F r) -> F {
            l.first = H.add(r.first, H.mul(r.second, l.first));
            l.second = H.mul(l.second, r.second);
            return l;
        };
        auto g = [&](ll t) -> F {
            F b = a;
            F c = {0, 1};
            while (t){
                if (t & 1) c = mul(c, b);
                t /= 2;
                b = mul(b, b);
            }
            return c;
        };
        rep(i, 0, N){
            if (i + M <= N){
                res[i] = H.get(i, i + M);
                continue;
            }
            F d = {H.get(i, N), H.pow[N - i]};
            d = mul(d, g((i + M) / N - 1));
            d = mul(d, {H.get(0, (i + M) % N), H.pow[(i + M) % N]});
            res[i] = d.first;
        }
        return res;
    };
    int ans = INF;
    rep(rp, 0, 2){
        auto A = f();
        reverse(all(S));
        auto B = f();
        reverse(all(B));
        rep(i, 0, N){
            if (A[i] == B[(i + M) % N]){
                chmin(ans, (int)(i + M - 1) / (int)N);
            }
        }
        M++;
    }
    if (ans == INF) cout << "-1\n";
    else cout << ans + 1 << "\n";
}