#include <bits/stdc++.h>
#define rep(i,n) for(ll i=0;i<(ll)(n);i++)
#define all(x) x.begin(), x.end()
using namespace std;
using ll=long long;
using ld=long double;
using P=pair<ll,ll>;
#include <atcoder/all>
using namespace atcoder;
//using mint=static_modint<998244353>;
using mint=static_modint<1000000007>;
////using mint=modint;
//#pragma GCC target("avx2")
//#pragma GCC optimize("O3")
//#pragma GCC optimize("unroll-loops")

int inf=2147483647;
ll INF=9223372036854775807;
const ld PI=acos(-1);

void yn(bool f){
	if(f)cout<<"Yes"<<endl;
	else cout<<"No"<<endl;
	return;
}

ll n,m;

bool in(int x,int y){
	if(x<0||n<=x)return false;
	if(y<0||m<=y)return false;
	return true;
}

vector<int> dx={1,-1,0,0};
vector<int> dy={0,0,1,-1};

bool isp(string s){
	rep(i,s.size())if(s[i]!=s[s.size()-1-i])return false;
	return true;
}

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

	if(isp(s)){
		cout<<(n+m-1)/n<<endl;
		return;
	}

	if(isp(s.substr(1,s.size()-1))||isp(s.substr(0,s.size()-1))){
		ll lb=0,ub=1e9;
		while(lb+1<ub){
			ll md=(lb+ub)/2;
			if(n*md>=m+1)ub=md;
			else lb=md;
		}
		cout<<ub<<endl;
		return;
	}

	else{
		ll ans=0;
		ll cru=0;
		int l=0,r=s.size()-1;
		while(s[l]==s[r]){
			l++;
			r--;
			cru+=2;
		}
		ans=max(ans,cru);
		l=1,r=s.size()-1;
		while(s[l]==s[r]){
			l++;
			r--;
			cru+=2;
		}
		ans=max(ans,cru);
		l=0,r=s.size()-2;
		while(s[l]==s[r]){
			l++;
			r--;
			cru+=2;
		}
		ans=max(ans,cru);
		if(ans>=m)cout<<2<<endl;
		else cout<<-1<<endl;
		return;
	}

}

int main(){
	ll n;cin>>n;
	rep(i,n)solve();
}