//何をすればいいかはすぐに分かるけど、偶数長回文があるためインデックス計算が大変
#include <iostream>
#include <algorithm>
#include <vector>
#include <string>
#define int long long
#define rep(i, n) for(i = 0; i < n; i++)
using namespace std;

vector<int> manacher(string S) {
	vector<int> R(S.size());
	int i = 0, j = 0;
	while (i < S.size()) {
	while (i-j >= 0 && i+j < S.size() && S[i-j] == S[i+j]) ++j;
	R[i] = j;
	int k = 1;
	while (i-k >= 0 && k+R[i-k] < j) R[i+k] = R[i-k], ++k;
	i += k; j -= k;
	}
	return R;
}

int solve(int n, int m, string s) {
	int i;

	string t = "-";
	rep(i, n) {
		t += s[i];
		t += '-';
	}
	vector<int> mana = manacher(t);

	//先頭i文字, 末尾n-i文字が回文かどうか
	const int INF = 1e+15;
	int ret = INF;
	rep(i, n) {
		//t[2 * i]にある$で分ける
		int c = 2 * i;
		if (mana[c - i] - 1 < i) continue;
		if (mana[c + n - i] - 1 < n - i) continue;
		int x = i;
		int y = n - i;
		int cnt = ((m + min(x, y)) + (x + y - 1)) / (x + y);
		ret = min(ret, cnt);
	}
	if (ret >= INF) return -1;
	return ret;
}

signed main() {
	int T;
	cin >> T;
	while (T--) {
		int n, m; string s;
		cin >> n >> m >> s;
		int res = solve(n, m, s);
		cout << res << endl;
	}
	return 0;
}