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

template <typename T>
vector<int> manacher(const T &s){
    int n = s.size();
    vector<int> rad(n);
    int i = 0, j = 0;
    while(i < n){
        while(i - j >= 0 && i + j < (int) s.size() && s[i - j] == s[i + j]){
            j++;
        }
        rad[i] = j;
        int k = 1;
        while(i - k >= 0 && i + k < n && k + rad[i - k] < j){
            rad[i + k] = rad[i - k];
            k++;
        }
        i += k;
        j -= k;
    }
    return rad;
}

struct PalindromeCheck{
    const string s;
    string t;
    int n;
    vector<int> mana;

    PalindromeCheck(const string &str) : s(str){
        n = s.size();
        t = "$";
        for(int i = 0; i < n; i++){
            t += s[i];
            t += "$";
        }
        mana = manacher(t);
    }

    // [l, r)
    bool isPalindrome(int l, int r) const {
        int mid = l + r;
        return r * 2 - mid - 1 < mana[mid];
    }
};

const long long INF = 1LL << 60;

void solve(){
    int n;
    long long m;
    cin >> n >> m;
    string s;
    cin >> s;

    string u = "";
    {
        for(int i = 1; i <= 2; i++){
            u += s;
            int len = u.size();
            PalindromeCheck pc(u);
            for(int j = 0; j < len - m + 1; j++){
                if(pc.isPalindrome(j, j + m)){
                    cout << i << endl;
                    return;
                }
            }
            for(int j = 0; j < len - m; j++){
                if(pc.isPalindrome(j, j + m + 1)){
                    cout << i << endl;
                    return;
                }
            }
        }
    }

    long long ans = INF;
    PalindromeCheck pc(u);
    for(int i = 0; i < n; i++){
        for(int j = n; j <= n + 1; j++){
            if(pc.isPalindrome(i, i + j)){
                long long l = -1, r = -1;
                if(j % 2){
                    long long need = m / 2;
                    l = i + j / 2 - need, r = i + j / 2 + need;
                }else{
                    long long need = (m + 1) / 2;
                    l = i + j / 2 - need, r = i + j / 2 + need - 1;
                }

                // 二分探索使わなくてもできるはず。。。
                long long ok = 1e9, ng = -1;
                while(abs(ok - ng) > 1){
                    long long mid = (ok + ng) / 2;
                    if(l + mid * n >= 0){
                        ok = mid;
                    }else{
                        ng = mid;
                    }
                }
                l += ok * n, r += ok * n;

                ans = min(ans, 1LL + r / n);
            }
        }
    }

    if(ans == INF){
        cout << -1 << endl;
    }else{
        cout << ans << endl;
    }
}

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

    int T; cin >> T;
    while(T--){
        solve();
    }
}