#include <stdio.h>
#include <bits/stdc++.h>
#include <atcoder/all>
using namespace atcoder;
using mint = modint998244353;
using namespace std;
#define rep(i,n) for (int i = 0; i < (n); ++i)
#define Inf32 1000000001
#define Inf64 1000000000000000001

struct rolling_hash{

	long long t_hash;
	static inline vector<long long> power;
	static const long long MOD = (1LL<<61)-1;
	static const long long b = 123456;
	int sz;
	
	rolling_hash(){		
		sz = 0;
		t_hash = 0;
	}
	
	rolling_hash(char c){
		sz = 1;
		t_hash = b*c;
	}

	long long mul(__int128 x,__int128 y){
		__int128 t = x*y;
		t = (t>>61) + (t&MOD);
		
		if(t>=MOD)t -= MOD;
		return t;
	}
	
	long long get_pow(int sz){
		if(power.size()>sz)return power[sz];
		
		while(power.size()<=sz){
			if(power.size()==0)power.push_back(1);
			else power.push_back(mul(power.back(),b));
		}
		return power.back();
		
	}
	
	rolling_hash &operator+=(const rolling_hash &another){
		
		(*this).t_hash = mul((*this).t_hash,get_pow(another.sz));
		(*this).t_hash += another.t_hash;
		if((*this).t_hash>=MOD)(*this).t_hash -= MOD;
			
		(*this).sz += another.sz;
		
		return (*this);
	}
	
	rolling_hash operator+(const rolling_hash &another)const{
		return (rolling_hash(*this)+=another);
	}
	
	rolling_hash &operator-=(const rolling_hash &another){

		(*this).t_hash += MOD - mul(another.t_hash,get_pow((*this).sz-another.sz));
		if((*this).t_hash>=MOD)(*this).t_hash -= MOD;
			
		(*this).sz -= another.sz;

		return (*this);
	}
	
	rolling_hash operator-(const rolling_hash &another)const{
		return (rolling_hash(*this)-=another);
	}
	
	bool operator<(const rolling_hash &another)const{
		if((*this).t_hash!=another.t_hash)return (*this).t_hash<another.t_hash;
		return (*this).sz<another.sz;
	}
	
	bool operator==(const rolling_hash &another)const{
		return ((*this).t_hash==another.t_hash && (*this).sz==another.sz);
	}

	
};
void solve(){
	long long n,m;
	cin>>n>>m;
	string S;
	cin>>S;
	S = S+S+S+S;
	vector<rolling_hash> h(n*4+1), rh(n*4+1);
	//cout<<'a'<<endl;
	rep(i,n*4){
		h[i+1] = h[i]+rolling_hash(S[i]);
		rh[i+1] = rh[i]+rolling_hash(S[n*4-i-1]);
	}
	//cout<<'b'<<endl;
	long long ans = Inf64;
	rep(i,n){
		int ok = 0,ng = n+1;
		while(ng-ok>1){
			int mid = (ok+ng)/2;
			int l = n+i;
			int r = l+1;
			l -= mid,r += mid;
			if(h[r]-h[l]==rh[n*4-l]-rh[n*4-r])ok = mid;
			else ng = mid;
		}
		if(ok==n||ok*2+1 >= m){
			long long mm = m;
			if(mm%2==0)mm++;
			long long l = i - mm/2;
			long long r = l + mm;
			if(l<0){
				long long D  =-l;
				D = (D+n-1)/n;
				l += D*n, r+=D*n;
			}
			ans = min((r+n-1)/n, ans);
		}
	}
	rep(i,n){
		if(S[i]!=S[i+1])continue;
		int ok = 0,ng = n+1;
		while(ng-ok>1){
			int mid = (ok+ng)/2;
			int l = n+i;
			int r = l+2;
			l -= mid,r += mid;
			if(h[r]-h[l]==rh[n*4-l]-rh[n*4-r])ok = mid;
			else ng = mid;
		}
		if(ok==n||ok*2+2 >= m){
			long long mm = m;
			if(mm%2==1)mm++;
			long long l = i - (mm-2)/2;
			long long r = l + mm;
			if(l<0){
				long long D  =-l;
				D = (D+n-1)/n;
				l += D*n, r+=D*n;
			}
			ans = min((r+n-1)/n, ans);
		}
	}
	if(ans==Inf64)ans = -1;
	cout<<ans<<endl;
}
int main(){
	int _t;
	cin>>_t;
	rep(_,_t)solve();
	
    return 0;
}