#include<bits/stdc++.h>
#include<atcoder/all>
#define rep(i,n) for(int i=0;i<n;i++)
using namespace std;
using namespace atcoder;
typedef long long ll;
typedef vector<int> vi;
typedef vector<long long> vl;
typedef vector<vector<int>> vvi;
typedef vector<vector<long long>> vvl;
typedef long double ld;
typedef pair<int, int> P;

ostream& operator<<(ostream& os, const modint& a) {os << a.val(); return os;}
template <int m> ostream& operator<<(ostream& os, const static_modint<m>& a) {os << a.val(); return os;}
template <int m> ostream& operator<<(ostream& os, const dynamic_modint<m>& a) {os << a.val(); return os;}
template<typename T> istream& operator>>(istream& is, vector<T>& v){int n = v.size(); assert(n > 0); rep(i, n) is >> v[i]; return is;}
template<typename U, typename T> ostream& operator<<(ostream& os, const pair<U, T>& p){os << p.first << ' ' << p.second; return os;}
template<typename T> ostream& operator<<(ostream& os, const vector<T>& v){int n = v.size(); rep(i, n) os << v[i] << (i == n - 1 ? "\n" : " "); return os;}
template<typename T> ostream& operator<<(ostream& os, const vector<vector<T>>& v){int n = v.size(); rep(i, n) os << v[i] << (i == n - 1 ? "\n" : ""); return os;}
template<typename T> ostream& operator<<(ostream& os, const set<T>& se){for(T x : se) os << x << " "; os << "\n"; return os;}
template<typename T> ostream& operator<<(ostream& os, const unordered_set<T>& se){for(T x : se) os << x << " "; os << "\n"; return os;}
template<typename S, auto op, auto e> ostream& operator<<(ostream& os, const atcoder::segtree<S, op, e>& seg){int n = seg.max_right(0, [](S){return true;}); rep(i, n) os << seg.get(i) << (i == n - 1 ? "\n" : " "); return os;}
template<typename S, auto op, auto e, typename F, auto mapping, auto composition, auto id> ostream& operator<<(ostream& os, const atcoder::lazy_segtree<S, op, e, F, mapping, composition, id>& seg){int n = seg.max_right(0, [](S){return true;}); rep(i, n) os << seg.get(i) << (i == n - 1 ? "\n" : " "); return os;}

template<typename T> void chmin(T& a, T b){a = min(a, b);}
template<typename T> void chmax(T& a, T b){a = max(a, b);}

// thanks for snuke-san's blog
// https://snuke.hatenablog.com/entry/2014/12/02/235837
vector<int> manacher(vector<int>& s){
	int n = s.size();
	vector<int> res(n);
	int i = 0, j = 0;
	while(i < n){
		while(i - j >= 0 && i + j < n && s[i-j] == s[i+j]) ++j;
		res[i] = j;
		int k = 1;
		while(i - k >= 0 && k + res[i-k] < j) res[i+k] = res[i-k], ++k;
		i += k; j -= k;
	}
	return res;
}

vector<int> manacher(string& s){
	vector<int> s_int;
	for(char c : s) s_int.push_back(c);
	return manacher(s_int);
}

int solve(){
	int n, m;
	cin >> n >> m;
	string s;
	cin >> s;
	vector<int> history = {0};
	for(int time = 1; time <= 10; time++){
		string t;
		rep(_, time){
			rep(i, n){
				t += s[i];
				t += '_';
			}
		}
		auto vec = manacher(t);
		int x = 0;
		rep(i, n * time){
			chmax(x, 1 + (vec[2 * i] - 1) / 2 * 2);
		}
		rep(i, n * time){
			chmax(x, vec[2 * i + 1] / 2 * 2);
		}
		history.push_back(x);
		if(x >= m){
			cout << time << ' ' << "\n";
			return 0;
		}
	}
	if(history[3] == history[4] and history[4] == history[5]){
		cout << "-1\n";
		return 0;
	}
	long long ok = 5 * m, ng = 5;
	while(ok - ng > 1){
		long long mid = (ok + ng) / 2;
		long long x = history[3];
		long long diff = mid - 3;
		x += diff / 2 * (history[5] - history[3]);
		if(diff % 2) x += history[4] - history[3];
		if(x >= m) ok = mid;
		else ng = mid;
	}
//	if(ok == 5 * m) assert(false);
	cout << ok << "\n";
	return 0;
}

int main(){
	int t;
	cin >> t;
	rep(_, t) solve();
	
	return 0;
}