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

struct RollingHash{
    long long BASE = 257, RMOD = (1ll<<61)-1;
    long long MASK31 = (1ll<<31)-1, MASK30 = (1ll<<30)-1;
    int n;
    std::vector<long long> dat, dat2, base_pow;
    RollingHash()  {}
    RollingHash(std::string &s) : n(s.size()), dat(n+1), dat2(n+1), base_pow(n+1) {
        base_pow[0] = 1;
        for(int i = 0; i < n; i++){
            dat[i+1] = safe_mod(internal_mul(dat[i], BASE) + s[i]);
            dat2.rbegin()[i+1] = safe_mod(internal_mul(dat2.rbegin()[i], BASE) + s.rbegin()[i]);
            base_pow[i+1] = internal_mul(base_pow[i], BASE);
        }
    }
    long long internal_mul(long long a, long long b){
        long long au = a >> 31, ad = a & MASK31;
        long long bu = b >> 31, bd = b & MASK31;
        long long mid = ad * bu + au * bd;
        long long midu = mid >> 30;
        long long midd = mid & MASK30;
        return safe_mod(au * bu * 2 + midu + (midd << 31) + ad * bd);
    }
    long long safe_mod(long long x){
        long long xu = x >> 61, xd = x & RMOD;
        long long res = xu + xd;
        if (res >= RMOD) res -= RMOD;
        return res;
    }
    long long hash(int l, int r){
        long long res = dat[r] - internal_mul(dat[l], base_pow[r - l]);
        if(res < 0)res += RMOD;
        return res;
    }
    long long revhash(int l, int r){
        long long res = dat2[l] - internal_mul(dat2[r], base_pow[r - l]);
        if(res < 0)res += RMOD;
        return res;
    }
    long long joint(long long lhs, long long rhs, long long rsize){
        long long res = internal_mul(lhs, base_pow[rsize]) + rhs;
        if(res >= RMOD) res -= RMOD;
        return res;
    }
};

bool para(string &s){
    int l = 0, r = s.size() - 1;
    while(l < r){
        if(s[l] != s[r]) return false;
        l++, r--;
    }
    return true;
}

int check(string &s){
    int n = s.size();
    RollingHash RH(s);
    int ans = 0;
    for(int i = 0; i < n; i++){
        int ok = 0, ng = min(i, n - 1 - i) + 1;
        while(ok + 1 < ng){
            int mid = (ok + ng) / 2;
            if(RH.hash(i - mid, i) == RH.revhash(i + 1, i + 1 + mid)) ok = mid;
            else ng = mid;
        }
        ans = max(ans, 1 + ok * 2);
    }
    for(int i = 1; i < n; i++){
        int ok = 0, ng = min(i, n - i) + 1;
        while(ok + 1 < ng){
            int mid = (ok + ng) / 2;
            if(RH.hash(i - mid, i) == RH.revhash(i, i + mid)) ok = mid;
            else ng = mid;
        }
        ans = max(ans, ok * 2);
    }
    return ans;
}

int main(){
    ios::sync_with_stdio(false);
    cin.tie(0);
    int T;
    cin >> T;
    while(T--){
        int n, m;
        string s;
        cin >> n >> m >> s;
        if(para(s)){
            cout << (m + n - 1) / n << '\n';
            continue;
        }
        string t = s;
        if(check(t) >= m){
            cout << 1 << '\n';
            continue;
        }
        t += s;
        if(check(t) >= m){
            cout << 2 << '\n';
            continue;
        }
        t += s;
        if(check(t) >= m){
            cout << 3 << '\n';
            continue;
        }
        t += s;
        if(check(t) >= m){
            cout << 4 << '\n';
            continue;
        }
        cout << -1 << '\n';
    }
}