#include <bits/stdc++.h>
#ifdef LOCAL
#include <debug.hpp>
#else
#define debug(...) void(0)
#endif

namespace atcoder {

namespace internal {

std::vector<int> sa_naive(const std::vector<int>& s) {
    int n = int(s.size());
    std::vector<int> sa(n);
    std::iota(sa.begin(), sa.end(), 0);
    std::sort(sa.begin(), sa.end(), [&](int l, int r) {
        if (l == r) return false;
        while (l < n && r < n) {
            if (s[l] != s[r]) return s[l] < s[r];
            l++;
            r++;
        }
        return l == n;
    });
    return sa;
}

std::vector<int> sa_doubling(const std::vector<int>& s) {
    int n = int(s.size());
    std::vector<int> sa(n), rnk = s, tmp(n);
    std::iota(sa.begin(), sa.end(), 0);
    for (int k = 1; k < n; k *= 2) {
        auto cmp = [&](int x, int y) {
            if (rnk[x] != rnk[y]) return rnk[x] < rnk[y];
            int rx = x + k < n ? rnk[x + k] : -1;
            int ry = y + k < n ? rnk[y + k] : -1;
            return rx < ry;
        };
        std::sort(sa.begin(), sa.end(), cmp);
        tmp[sa[0]] = 0;
        for (int i = 1; i < n; i++) {
            tmp[sa[i]] = tmp[sa[i - 1]] + (cmp(sa[i - 1], sa[i]) ? 1 : 0);
        }
        std::swap(tmp, rnk);
    }
    return sa;
}

// SA-IS, linear-time suffix array construction
// Reference:
// G. Nong, S. Zhang, and W. H. Chan,
// Two Efficient Algorithms for Linear Time Suffix Array Construction
template <int THRESHOLD_NAIVE = 10, int THRESHOLD_DOUBLING = 40>
std::vector<int> sa_is(const std::vector<int>& s, int upper) {
    int n = int(s.size());
    if (n == 0) return {};
    if (n == 1) return {0};
    if (n == 2) {
        if (s[0] < s[1]) {
            return {0, 1};
        } else {
            return {1, 0};
        }
    }
    if (n < THRESHOLD_NAIVE) {
        return sa_naive(s);
    }
    if (n < THRESHOLD_DOUBLING) {
        return sa_doubling(s);
    }

    std::vector<int> sa(n);
    std::vector<bool> ls(n);
    for (int i = n - 2; i >= 0; i--) {
        ls[i] = (s[i] == s[i + 1]) ? ls[i + 1] : (s[i] < s[i + 1]);
    }
    std::vector<int> sum_l(upper + 1), sum_s(upper + 1);
    for (int i = 0; i < n; i++) {
        if (!ls[i]) {
            sum_s[s[i]]++;
        } else {
            sum_l[s[i] + 1]++;
        }
    }
    for (int i = 0; i <= upper; i++) {
        sum_s[i] += sum_l[i];
        if (i < upper) sum_l[i + 1] += sum_s[i];
    }

    auto induce = [&](const std::vector<int>& lms) {
        std::fill(sa.begin(), sa.end(), -1);
        std::vector<int> buf(upper + 1);
        std::copy(sum_s.begin(), sum_s.end(), buf.begin());
        for (auto d : lms) {
            if (d == n) continue;
            sa[buf[s[d]]++] = d;
        }
        std::copy(sum_l.begin(), sum_l.end(), buf.begin());
        sa[buf[s[n - 1]]++] = n - 1;
        for (int i = 0; i < n; i++) {
            int v = sa[i];
            if (v >= 1 && !ls[v - 1]) {
                sa[buf[s[v - 1]]++] = v - 1;
            }
        }
        std::copy(sum_l.begin(), sum_l.end(), buf.begin());
        for (int i = n - 1; i >= 0; i--) {
            int v = sa[i];
            if (v >= 1 && ls[v - 1]) {
                sa[--buf[s[v - 1] + 1]] = v - 1;
            }
        }
    };

    std::vector<int> lms_map(n + 1, -1);
    int m = 0;
    for (int i = 1; i < n; i++) {
        if (!ls[i - 1] && ls[i]) {
            lms_map[i] = m++;
        }
    }
    std::vector<int> lms;
    lms.reserve(m);
    for (int i = 1; i < n; i++) {
        if (!ls[i - 1] && ls[i]) {
            lms.push_back(i);
        }
    }

    induce(lms);

    if (m) {
        std::vector<int> sorted_lms;
        sorted_lms.reserve(m);
        for (int v : sa) {
            if (lms_map[v] != -1) sorted_lms.push_back(v);
        }
        std::vector<int> rec_s(m);
        int rec_upper = 0;
        rec_s[lms_map[sorted_lms[0]]] = 0;
        for (int i = 1; i < m; i++) {
            int l = sorted_lms[i - 1], r = sorted_lms[i];
            int end_l = (lms_map[l] + 1 < m) ? lms[lms_map[l] + 1] : n;
            int end_r = (lms_map[r] + 1 < m) ? lms[lms_map[r] + 1] : n;
            bool same = true;
            if (end_l - l != end_r - r) {
                same = false;
            } else {
                while (l < end_l) {
                    if (s[l] != s[r]) {
                        break;
                    }
                    l++;
                    r++;
                }
                if (l == n || s[l] != s[r]) same = false;
            }
            if (!same) rec_upper++;
            rec_s[lms_map[sorted_lms[i]]] = rec_upper;
        }

        auto rec_sa =
            sa_is<THRESHOLD_NAIVE, THRESHOLD_DOUBLING>(rec_s, rec_upper);

        for (int i = 0; i < m; i++) {
            sorted_lms[i] = lms[rec_sa[i]];
        }
        induce(sorted_lms);
    }
    return sa;
}

}  // namespace internal

std::vector<int> suffix_array(const std::vector<int>& s, int upper) {
    assert(0 <= upper);
    for (int d : s) {
        assert(0 <= d && d <= upper);
    }
    auto sa = internal::sa_is(s, upper);
    return sa;
}

template <class T> std::vector<int> suffix_array(const std::vector<T>& s) {
    int n = int(s.size());
    std::vector<int> idx(n);
    iota(idx.begin(), idx.end(), 0);
    sort(idx.begin(), idx.end(), [&](int l, int r) { return s[l] < s[r]; });
    std::vector<int> s2(n);
    int now = 0;
    for (int i = 0; i < n; i++) {
        if (i && s[idx[i - 1]] != s[idx[i]]) now++;
        s2[idx[i]] = now;
    }
    return internal::sa_is(s2, now);
}

std::vector<int> suffix_array(const std::string& s) {
    int n = int(s.size());
    std::vector<int> s2(n);
    for (int i = 0; i < n; i++) {
        s2[i] = s[i];
    }
    return internal::sa_is(s2, 255);
}

// Reference:
// T. Kasai, G. Lee, H. Arimura, S. Arikawa, and K. Park,
// Linear-Time Longest-Common-Prefix Computation in Suffix Arrays and Its
// Applications
template <class T>
std::vector<int> lcp_array(const std::vector<T>& s,
                           const std::vector<int>& sa) {
    int n = int(s.size());
    assert(n >= 1);
    std::vector<int> rnk(n);
    for (int i = 0; i < n; i++) {
        rnk[sa[i]] = i;
    }
    std::vector<int> lcp(n - 1);
    int h = 0;
    for (int i = 0; i < n; i++) {
        if (h > 0) h--;
        if (rnk[i] == 0) continue;
        int j = sa[rnk[i] - 1];
        for (; j + h < n && i + h < n; h++) {
            if (s[j + h] != s[i + h]) break;
        }
        lcp[rnk[i] - 1] = h;
    }
    return lcp;
}

std::vector<int> lcp_array(const std::string& s, const std::vector<int>& sa) {
    int n = int(s.size());
    std::vector<int> s2(n);
    for (int i = 0; i < n; i++) {
        s2[i] = s[i];
    }
    return lcp_array(s2, sa);
}

// Reference:
// D. Gusfield,
// Algorithms on Strings, Trees, and Sequences: Computer Science and
// Computational Biology
template <class T> std::vector<int> z_algorithm(const std::vector<T>& s) {
    int n = int(s.size());
    if (n == 0) return {};
    std::vector<int> z(n);
    z[0] = 0;
    for (int i = 1, j = 0; i < n; i++) {
        int& k = z[i];
        k = (j + z[j] <= i) ? 0 : std::min(j + z[j] - i, z[i - j]);
        while (i + k < n && s[k] == s[i + k]) k++;
        if (j + z[j] < i + z[i]) j = i;
    }
    z[0] = n;
    return z;
}

std::vector<int> z_algorithm(const std::string& s) {
    int n = int(s.size());
    std::vector<int> s2(n);
    for (int i = 0; i < n; i++) {
        s2[i] = s[i];
    }
    return z_algorithm(s2);
}

}  // namespace atcoder

std::vector<int> Manacher(const std::string& s) {
    int n = s.size();
    std::vector<int> res(n);
    for (int i = 0, j = 0; i < n;) {
        while (i - j >= 0 and i + j < n and s[i - j] == s[i + j]) j++;
        res[i] = j;
        int k = 1;
        while (i - k >= 0 and i + k < n and k + res[i - k] < j) res[i + k] = res[i - k], k++;
        i += k;
        j -= k;
    }
    return res;
}

std::vector<int> PalindromeTable(const std::string& s) {
    int n = s.size();
    std::string t(n * 2 + 1, '$');
    for (int i = 0; i < n; i++) t[i * 2 + 1] = s[i];
    std::vector<int> v = Manacher(t), res;
    for (int i = 1; i < n * 2; i++) res.emplace_back(v[i] - 1);
    return res;
}

using namespace std;

typedef long long ll;
#define all(x) begin(x), end(x)
constexpr int INF = (1 << 30) - 1;
constexpr long long IINF = (1LL << 60) - 1;
constexpr int dx[4] = {1, 0, -1, 0}, dy[4] = {0, 1, 0, -1};

template <class T> istream& operator>>(istream& is, vector<T>& v) {
    for (auto& x : v) is >> x;
    return is;
}

template <class T> ostream& operator<<(ostream& os, const vector<T>& v) {
    auto sep = "";
    for (const auto& x : v) os << exchange(sep, " ") << x;
    return os;
}

template <class T, class U = T> bool chmin(T& x, U&& y) { return y < x and (x = forward<U>(y), true); }

template <class T, class U = T> bool chmax(T& x, U&& y) { return x < y and (x = forward<U>(y), true); }

template <class T> void mkuni(vector<T>& v) {
    sort(begin(v), end(v));
    v.erase(unique(begin(v), end(v)), end(v));
}

template <class T> int lwb(const vector<T>& v, const T& x) { return lower_bound(begin(v), end(v), x) - begin(v); }

template <typename T> struct SparseTable {
    typedef function<T(T, T)> F;
    vector<vector<T>> dat;
    vector<int> lookup;
    const F f;
    SparseTable(F f) : f(f) {}
    void build(const vector<T>& v) {
        int n = v.size(), h = 1;
        while ((1 << h) <= n) h++;
        dat.assign(h, vector<T>(n));
        lookup.assign(n + 1, 0);
        for (int i = 2; i <= n; i++) lookup[i] = lookup[i >> 1] + 1;
        for (int j = 0; j < n; j++) dat[0][j] = v[j];
        for (int i = 1, mask = 1; i < h; i++, mask <<= 1) {
            for (int j = 0; j < n; j++) {
                dat[i][j] = f(dat[i - 1][j], dat[i - 1][min(j + mask, n - 1)]);
            }
        }
    }
    T query(int a, int b) {
        int d = lookup[b - a];
        return f(dat[d][a], dat[d][b - (1 << d)]);
    }
};

void solve() {
    int n, K;
    string S;
    cin >> n >> K >> S;

    string T = S;
    reverse(all(T));
    string U = S + T;
    auto sa = atcoder::suffix_array(U);
    auto lcp = atcoder::lcp_array(U, sa);
    SparseTable<int> st([](int l, int r) { return min(l, r); });
    vector<int> pos(sa.size());
    for (int i = 0; i < int(sa.size()); i++) pos[sa[i]] = i;
    st.build(lcp);
    auto f = [&](int l, int r) {  // S[l] から左に続く文字と S[r] から右に続く文字の lcp
        if (l < -1) return -INF;
        if (n < r) return -INF;
        if (l == -1 or r == n) return 0;
        int res = min(l + 1, n - r);
        int L = r, R = 2 * n - 1 - l;
        L = pos[L], R = pos[R];
        if (L > R) swap(L, R);
        return min(res, st.query(L, R));
    };
    auto table = PalindromeTable(S);
    int ans = 0;
    for (int i = 0, j = 0; i < n; i++, j += 2) {  // S[i] を中心とする回文
        int len = table[j];
        int l = i - (len + 1) / 2, r = i + (len + 1) / 2;
        chmax(ans, len);
        for (int k = 1; k <= K; k++) {
            if (l - k >= -1) {
                chmax(ans, len + 2 * k + f(l - k, r));
            }
            if (r + k <= n) {
                chmax(ans, len + 2 * k + f(l, r + k));
            }
        }
    }
    for (int i = 0, j = 1; i + 1 < n; i++, j += 2) {  // S[i] と S[i + 1] の間を中心とする回文
        int len = table[j];
        int l = i - len / 2, r = (i + 1) + len / 2;
        chmax(ans, len);
        for (int k = 1; k <= K; k++) {
            if (l - k >= -1) {
                chmax(ans, len + k + f(l - k, r));
            }
            if (r + k <= n) {
                chmax(ans, len + k + f(l, r + k));
            }
        }
    }
    for (int i = -1; i < n; i++) {
        for (int k = 0; k <= K; k++) {
            int p = k, q = K - k;
            int l = i, r = i + 1;
            if (p < q)
                l -= q - p;
            else
                r += p - q;
            chmax(ans, max(p, q) * 2 + f(l, r));
            // debug(i, k, l, r, f(l, r), max(p, q) * 2 + f(l, r));
        }
    }
    for (int i = -1; i < n; i++) {
        for (int k = 0; k <= K - 1; k++) {
            int p = k, q = K - 1 - k;
            int l = i, r = i + 1;
            if (p < q)
                l -= q - p;
            else
                r += p - q;
            chmax(ans, max(p, q) * 2 + 1 + f(l, r));
            // debug(i, k, l, r, f(l, r), max(p, q) * 2 + 1 + f(l, r));
        }
    }

    cout << ans << '\n';
}

int main() {
    ios::sync_with_stdio(false);
    cin.tie(nullptr);
    int t;
    cin >> t;
    for (; t--;) solve();
    return 0;
}