#line 1 "main.cpp"
#include<bits/stdc++.h>
using namespace std;
// #pragma GCC target("avx,avx2")
// #pragma GCC optimize("O3")
// #pragma GCC optimize("unroll-loops")
#ifdef LOCAL
#include <debug.hpp>
#define debug(...) debug_print::multi_print(#__VA_ARGS__, __VA_ARGS__)
#else
#define debug(...) (static_cast<void>(0))
#endif
using namespace std;
using ll = long long;
using ull = unsigned long long;
using ld = long double;
using pll = pair<ll,ll>;
using pii = pair<int,int>;
using vi = vector<int>;
using vvi = vector<vi>;
using vvvi = vector<vvi>;
using vl = vector<ll>;
using vvl = vector<vl>;
using vvvl = vector<vvl>;
using vul = vector<ull>;
using vpii = vector<pii>;
using vvpii = vector<vpii>;
using vpll = vector<pll>;
using vs = vector<string>;
template<class T> using pq = priority_queue<T,vector<T>, greater<T>>;
#define overload4(_1, _2, _3, _4, name, ...) name
#define overload3(a,b,c,name,...) name
#define rep1(n) for (ll UNUSED_NUMBER = 0; UNUSED_NUMBER < (n); ++UNUSED_NUMBER)
#define rep2(i, n) for (ll i = 0; i < (n); ++i)
#define rep3(i, a, b) for (ll i = (a); i < (b); ++i)
#define rep4(i, a, b, c) for (ll i = (a); i < (b); i += (c))
#define rep(...) overload4(__VA_ARGS__, rep4, rep3, rep2, rep1)(__VA_ARGS__)
#define rrep1(n) for(ll i = (n) - 1;i >= 0;i--)
#define rrep2(i,n) for(ll i = (n) - 1;i >= 0;i--)
#define rrep3(i,a,b) for(ll i = (b) - 1;i >= (a);i--)
#define rrep4(i,a,b,c) for(ll i = (a) + ((b)-(a)-1) / (c) * (c);i >= (a);i -= c)
#define rrep(...) overload4(__VA_ARGS__, rrep4, rrep3, rrep2, rrep1)(__VA_ARGS__)
#define all1(i) begin(i) , end(i)
#define all2(i,a) begin(i) , begin(i) + a
#define all3(i,a,b) begin(i) + a , begin(i) + b
#define all(...) overload3(__VA_ARGS__, all3, all2, all1)(__VA_ARGS__)
#define sum(...) accumulate(all(__VA_ARGS__),0LL)
template<class T> bool chmin(T &a, const T &b){ if(a > b){ a = b; return 1; } else return 0; }
template<class T> bool chmax(T &a, const T &b){ if(a < b){ a = b; return 1; } else return 0; }
template<class T> auto min(const T& a){return *min_element(all(a));}
template<class T> auto max(const T& a){return *max_element(all(a));}
template<class... Ts> void in(Ts&... t);
#define INT(...) int __VA_ARGS__; in(__VA_ARGS__)
#define LL(...) ll __VA_ARGS__; in(__VA_ARGS__)
#define STR(...) string __VA_ARGS__; in(__VA_ARGS__)
#define CHR(...) char __VA_ARGS__; in(__VA_ARGS__)
#define DBL(...) double __VA_ARGS__; in(__VA_ARGS__)
#define LD(...) ld __VA_ARGS__; in(__VA_ARGS__)
#define VEC(type, name, size) vector<type> name(size); in(name)
#define VV(type, name, h, w) vector<vector<type>> name(h, vector<type>(w)); in(name)
ll intpow(ll a, ll b){ll ans = 1; while(b){if(b & 1) ans *= a; a *= a; b /= 2;} return ans;}
ll modpow(ll a, ll b, ll p){ ll ans = 1; a %= p;if(a < 0) a += p;while(b){ if(b & 1) (ans *= a) %= p; (a *= a) %= p; b /= 2; } return ans; }
bool is_clamp(ll val,ll low,ll high) {return low <= val && val < high;}
void Yes() {cout << "Yes\n";return;}
void No() {cout << "No\n";return;}
void YES() {cout << "YES\n";return;}
void NO() {cout << "NO\n";return;}
template <typename T>
T floor(T a, T b) {return a / b - (a % b && (a ^ b) < 0);}
template <typename T>
T ceil(T x, T y) {return floor(x + y - 1, y);}
template <typename T>
T bmod(T x, T y) {return x - y * floor(x, y);}
template <typename T>
pair<T, T> divmod(T x, T y) {T q = floor(x, y);return {q, x - q * y};}
namespace IO{
#define VOID(a) decltype(void(a))
struct setting{ setting(){cin.tie(nullptr); ios::sync_with_stdio(false);fixed(cout); cout.precision(15);}} setting;
template<int I> struct P : P<I-1>{};
template<> struct P<0>{};
template<class T> void i(T& t){ i(t, P<3>{}); }
void i(vector<bool>::reference t, P<3>){ int a; i(a); t = a; }
template<class T> auto i(T& t, P<2>) -> VOID(cin >> t){ cin >> t; }
template<class T> auto i(T& t, P<1>) -> VOID(begin(t)){ for(auto&& x : t) i(x); }
template<class T, size_t... idx> void ituple(T& t, index_sequence<idx...>){in(get<idx>(t)...);}
template<class T> auto i(T& t, P<0>) -> VOID(tuple_size<T>{}){ituple(t, make_index_sequence<tuple_size<T>::value>{});} 
#undef VOID
}
#define unpack(a) (void)initializer_list<int>{(a, 0)...}
template<class... Ts> void in(Ts&... t){ unpack(IO :: i(t)); }
#undef unpack
constexpr long double PI = 3.141592653589793238462643383279L;
template <class F> struct REC {
    F f;
    REC(F &&f_) : f(forward<F>(f_)) {}
    template <class... Args> auto operator()(Args &&...args) const { return f(*this, forward<Args>(args)...); }};

constexpr int mod = 998244353;
//constexpr int mod = 1000000007;
#line 2 "library/string/manacher.hpp"
template<typename T>
vector<int> manacher(T s,bool calc_even = true) {
    if(calc_even) {
        int n = (int)s.size();
        assert(n > 0);
        s.resize(2 * n - 1);
        for(int i = n - 1; i >= 0; i--) {
            s[2 * i] = s[i];
        }
        auto d = *min_element(begin(s), end(s));
        for(int i = 0; i < n - 1; i++) {
            s[2 * i + 1] = d;
        }
    }
    int n = (int)s.size();
    vector<int> rad(n);
    int i = 0, j = 0;
    while(i < n) {
        while(i - j >= 0 && i + j < n && s[i - j] == s[i + j]) ++j;
        rad[i] = j;
        int k = 1;
        while(i - k >= 0 && i + k < n && k + rad[i - k] < j) {
            rad[i + k] = rad[i - k];
            ++k;
        }
        i += k, j -= k;
    }

    if(calc_even) {
        for(int i = 0; i < n; i++) {
            if(((i ^ rad[i]) & 1) == 0) rad[i]--;
        }
    } else {
        for(auto &&x: rad) x = 2 * x - 1;
    }
  return rad;
}
#line 2 "library/inner/inner-hash.hpp"
namespace inner {
    using i64 = long long;
    using u64 = unsigned long long;
    using u128 = __int128_t;
    template <int BASE_NUM = 2>
    struct Hash: array<u64, BASE_NUM> {
        using array<u64, BASE_NUM>::operator[];
        static constexpr int n = BASE_NUM;

        Hash():array<u64, BASE_NUM>() {}

        static constexpr u64 md = (1ull << 61) - 1;

        constexpr static Hash set(const i64 &a) {
            Hash res;
            fill(begin(res),end(res),cast(a));
            return res;
        }

        Hash &operator+=(const Hash &r) {
            for(int i = 0;i < n; i++) {
                if(((*this)[i] += r[i]) >= md) (*this)[i] -= md;
            }
            return *this;
        }
        Hash &operator+=(const i64 &r) {
            u64 s = cast(r);
            for (int i = 0; i < n; i++) {
                if (((*this)[i] += s) >= md) (*this)[i] -= md;
            }
            return *this;
        }
        Hash &operator-=(const Hash &r) {
            for (int i = 0; i < n; i++) {
                if (((*this)[i] += md - r[i]) >= md) (*this)[i] -= md;
            }
            return *this;
        }
        Hash &operator-=(const i64 &r) {
            u64 s = cast(r);
            for (int i = 0; i < n; i++) {
                if (((*this)[i] += md - s) >= md) (*this)[i] -= md;
            }
            return *this;
        }
        Hash &operator*=(const Hash &r) {
            for (int i = 0; i < n; i++) {
                (*this)[i] = modmul((*this)[i], r[i]);
            }
            return *this;
        }
        Hash &operator*=(const i64 &r) {
            u64 s = cast(r);
            for (int i = 0; i < n; i++) {
                (*this)[i] = modmul((*this)[i], s);
            }
            return *this;
        }

        Hash operator+(const Hash &r) { return Hash(*this) += r; }
        Hash operator+(const i64 &r) { return Hash(*this) += r; }
        Hash operator-(const Hash &r) { return Hash(*this) -= r; }
        Hash operator-(const i64 &r) { return Hash(*this) -= r; }
        Hash operator*(const Hash &r) { return Hash(*this) *= r; }
        Hash operator*(const i64 &r) { return Hash(*this) *= r; }
        Hash operator-() const {
            Hash res;
            for (int i = 0; i < n; i++) {
                res[i] = (*this)[i] == 0 ? 0 : md - (*this)[i];
            }
            return res;
        }
        friend Hash pfma(const Hash &a, const Hash &b, const Hash &c) {
            Hash res;
            for (int i = 0; i < n; i++) {
                res[i] = modfma(a[i], b[i], c[i]);
            }
            return res;
        }
        // a * b + c (mod p)
        friend Hash pfma(const Hash &a, const Hash &b, const i64 &c) {
            Hash res;
            u64 s = cast(c);
            for (int i = 0; i < n; i++) {
                res[i] = modfma(a[i], b[i], s);
            }
            return res;
        }
        Hash pow(long long e) {
            Hash a{*this}, res{Hash::set(1)};
            for (; e; a *= a, e >>= 1) {
                if (e & 1) res *= a;
            }
            return res;
        }
        static Hash get_basis() {
            static auto rand_time =
            chrono::duration_cast<chrono::nanoseconds>(
            chrono::high_resolution_clock::now().time_since_epoch())
            .count();
            static mt19937_64 rng(rand_time);
            Hash h;
            for (int i = 0; i < n; i++) {
                while (isPrimitive(h[i] = rng() % (md - 1) + 1) == false);
            }
            return h;
        }

    private:
        static u64 modpow(u64 a, u64 b) {
            u64 r = 1;
            for (a %= md; b; a = modmul(a, a), b >>= 1) r = modmul(r, a);
            return r;
        }
        static bool isPrimitive(u64 x) {
            for (auto &d : vector<u64>{2, 3, 5, 7, 11, 13, 31, 41, 61, 151, 331, 1321})
            if (modpow(x, (md - 1) / d) <= 1) return false;
            return true;
        }
        static inline constexpr u64 cast(const long long &a) {
            return a < 0 ? a + md : a;
        }
        static inline constexpr u64 modmul(const u64 &a, const u64 &b) {
            u128 ret = u128(a) * b;
            ret = (ret & md) + (ret >> 61);
            return ret >= md ? ret - md : ret;
        }
        static inline constexpr u64 modfma(const u64 &a, const u64 &b, const u64 &c) {
            u128 ret = u128(a) * b + c;
            ret = (ret & md) + (ret >> 61);
            return ret >= md ? ret - md : ret;
        }
    };
}
#line 3 "library/string/Rolling-Hash.hpp"
template <typename Str, int BASE_NUM = 2>
struct RollingHash {
    using Hash = inner::Hash<BASE_NUM>;
    Str data;
    vector<Hash> hs,pw;
    int s;
    static Hash basis;

    RollingHash(const Str &S = Str()) {build(S);}
    void build(const Str &S) {
        data = S;
        s = S.size();
        hs.resize(s + 1);
        pw.resize(s + 1);
        pw[0] = Hash::set(1);
        hs[0] = Hash::set(0);
        for(int i = 1;i <= s; i++) {
            pw[i] = pw[i-1] * basis;
            hs[i] = pfma(hs[i-1],basis,S[i-1]);
        }
    }

    Hash get(int l,int r = -1) const{
        if(r == -1)r = s;
        return pfma(hs[l],-pw[r-l],hs[r]);
    }

    static Hash get_hash(const Str &T) {
        Hash ret = Hash::set(0);
        for(int i = 0;i < (int)T.size();i++) {
            ret = pfma(ret,basis,T[i]);
        }
        return ret;
    }
    // a + b の hash を返す
    // 引数 : a, b, b の長さ
    static Hash unite(Hash a, Hash b, long long bsize) {
        return pfma(a, basis.pow(bsize), b);
    }
    int find(Str &T, int lower = 0) const {
        auto ths = get_Hash(T);
        for(int i = lower; i <= s -(int)T.size();i++) {
            if(ths == get(i,i + (int)T.size())) return i;
        }  
        return -1;
    }
    friend int LCP(const RollingHash &a,RollingHash &b,int astart,int bstart) {
        int ok = 0,ng = min(a.size() - astart,b.size() - bstart) + 1;
        while (ok + 1 < ng) {
            int med = (ok + ng) / 2;
            (a.get(astart,med + astart) == b.get(bstart,med + bstart) ? ok:ng) = med;
        }
        return ok;
    }
    friend int strcmp(const RollingHash &a,RollingHash &b,int astart,int bstart,int aend = -1,int bend = -1) {
        if (aend == -1) aend = a.size();
        if (bend == -1) bend = b.size();
        if (aend - astart == bend - bstart) {
            if(a.get(astart,aend) == b.get(bstart,bend)) {
                return 0;
            }
        }
        else if(aend - astart < bend - bstart) {
            if(a.get(astart,aend) == b.get(bstart,bstart + aend - astart)) {
                return 1;
            }            
        }
        else {
            if(a.get(astart,astart + bend - bstart) == b.get(bstart,bend)) {
                return -1;
            }               
        }
        if (a.data[astart] < b.data[bstart]) {return 1;}
        else if (a.data[astart] > b.data[bstart]) {return -1;}
        int n = min<int>({LCP(a,b,astart,bstart),aend - astart,bend - bstart});
        return astart + n == aend ? bstart + n == bend ? 0 : 1
            : bstart + n == bend                    ? -1
            : a.data[astart + n] < b.data[bstart + n] ? 1
                                                : -1;
    }
    int size() const{return s;}
};
template <typename Str,int BASE_NUM>
typename RollingHash<Str,BASE_NUM>::Hash RollingHash<Str,BASE_NUM>::basis = inner::Hash<BASE_NUM>::get_basis();
#line 101 "main.cpp"
using roriha = RollingHash<string,2>;
void solve() {
    INT(n,m);
    STR(s);
    auto ret1 = manacher(s);
    if(max(ret1) >= m) {
        cout << 1 << '\n';
        return;
    }
    string t = s + s;
    auto ret2 = manacher(t);
    if(max(ret2) >= m) {
        cout << 2 << '\n';
        return;
    }
    assert(false);
    roriha rs(s);
    reverse(all(s));
    roriha rt(s);
    int ans = 2e9;
    rep(i,n) {
        if(rs.get(0,i) == rt.get(n-i,n) && rs.get(i,n) == rt.get(0,n-i)) {
            int M = max(i,n-i);
            int x = m / n;
            int rem = m % n;
            if(M >= rem) x++;
            else x += 2;
            chmin(ans,x);
        }
    }
    if(ans == (int)2e9) cout << -1 << '\n';
    else cout << ans << '\n';
}
int main() {
    INT(TT);
    while(TT--) solve();
}