#include <bits/stdc++.h>
#include <atcoder/all>
//using namespace std;
//using namespace atcoder;
//using mint = modint1000000007;
//const int mod = 1000000007;
using mint = atcoder::modint998244353;
const int mod = 998244353;
//const int INF = 1e9;
const long long LINF = 1e18;
#define rep(i, n) for (int i = 0; i < (n); ++i)
#define rep2(i,l,r)for(int i=(l);i<(r);++i)
#define rrep(i, n) for (int i = (n) - 1; i >= 0; --i)
#define rrep2(i,l,r)for(int i=(r) - 1;i>=(l);--i)
#define all(x) (x).begin(),(x).end()
#define allR(x) (x).rbegin(),(x).rend()
#define P pair<int,int>
template<typename A, typename B> inline bool chmax(A & a, const B & b) { if (a < b) { a = b; return true; } return false; }
template<typename A, typename B> inline bool chmin(A & a, const B & b) { if (a > b) { a = b; return true; } return false; }
namespace RangeSumMint {
	// 区間加算
	mint op(mint a, mint b) { return a + b; }
	mint e() { return 0; }
	using segtree = atcoder::segtree<mint, op, e>;
}
template<typename T>
class Rollinghash {
public:
	Rollinghash(const std::vector<T>&v, int base) :base(base) {
		build(v);
	}
	Rollinghash(const std::string &s, int base = 27) :base(base) {
		std::vector<int>v;
		for (auto c : s)v.push_back(c - 'a' + 1);
		build(v);
	}
	// rは区間内に収まらなくてもいい
	// lは区間内::todo...
	mint get(const long long l, const long long r) {
		long long width = r - l;
		long long h = std::min(width, (long long)size - l);
		long long b = ((width - h) / size) * size;
		long long t = width - h - b;
		mint hash = 0;
		if (h) {
			//std::cout << l << "_" << l + h << std::endl;
			hash += seg.prod(l, l + h) / pow[l];
			//std::cout << hash.val() << std::endl;
		}
		if (b) {
			//std::cout << 0 << "!" << size << std::endl;
			hash += seg.prod(0, size) * (atcoder::pow_mod(base.val(), b, mod) - 1) / (pow[size] - 1) * pow[h];
			//std::cout << hash.val() << std::endl;
		}
		if (t) {
			//std::cout << 0 << "?" << t << std::endl;
			hash += atcoder::pow_mod(base.val(), h + b, mod)*seg.prod(0, t);
			//std::cout << hash.val() << std::endl;
		}
		return hash;
	}
	void update(int index, T value) {
		seg.set(index, value * pow[index]);
	}
	void update(int index, char c) {
		update(index, c - 'a' + 1);
	}
private:
	int size;
	mint base;
	mint inv;
	RangeSumMint::segtree seg;
	std::vector<mint>pow;

	template<typename U>
	void build(const std::vector<U>&v) {
		inv = base.inv();
		size = v.size();

		pow.resize(size + 1);
		pow[0] = 1;
		for (int i = 0; i < size; ++i)pow[i + 1] = pow[i] * base;

		std::vector<mint>mv(size);
		for (int i = 0; i < size; ++i) {
			mv[i] = pow[i] * v[i];
		}
		seg = RangeSumMint::segtree(mv);
	}
};
int main() {
	std::ios::sync_with_stdio(false);
	std::cin.tie(nullptr);
	int t; std::cin >> t;
	const int base = 100;
	std::vector<mint>pow(200005);
	pow[0] = 1;
	rep2(i, 1, pow.size())pow[i] = pow[i - 1] * base;
	while (t--) {
		int n, m; std::cin >> n >> m;
		std::string s; std::cin >> s;
		auto t = s;
		reverse(all(t));
		long long ans = LINF;
		auto rhS = Rollinghash<std::string>(s, 100);
		auto rhT = Rollinghash<std::string>(t, 100);
		rep(i, n) {
			int sz = (m) / 2;
			int iR = (i + 1) % n;
			mint hR = rhS.get(iR, iR + sz);
			int iL = (i - 1 + n) % n;
			iL = n - 1 - iL;
			//std::cout << std::endl;
			mint hL = rhT.get(iL, iL + sz);
			//std::cout << hR.val() << "__" << hL.val() << std::endl;
			//break;
			if (hR != hL)continue;
			int tmp = 1;
			int l = sz - i;
			if (l > 0)tmp += (l + n - 1) / n;
			int r = sz - (n - 1 - i);//???
			if (r > 0)tmp += (r + n - 1) / n;
			chmin(ans, tmp);
		}
		rep(i, n) {
			int sz = (m + 1) / 2;
			int iR = (i + 0) % n;
			mint hR = rhS.get(iR, iR + sz);
			int iL = (i - 1 + n) % n;
			iL = n - 1 - iL;
			mint hL = rhT.get(iL, iL + sz);
			if (hR != hL)continue;
			int tmp = 0 != i;
			int l = sz - i;
			int r = 0 == i ? sz : sz - (n - i);
			//cout << l << " " << r << endl;
			if (l > 0)tmp += (l + n - 1) / n;
			if (r > 0)tmp += (r + n - 1) / n;
			//cout << i << endl;
			chmin(ans, tmp);
		}
		if (LINF == ans)ans = -1;
		std::cout << ans << std::endl;
	}
	return 0;
}