#include <bits/stdc++.h>

using i64 = long long;

struct SA {
    int n;
    std::vector<int> sa, rk, lc;

    SA(std::string s) {
        n = s.size();
        sa.resize(n);
        lc.resize(n - 1);
        rk.resize(n);
        std::iota(sa.begin(), sa.end(), 0);
        std::sort(sa.begin(), sa.end(),
            [&](int a, int b) {
                return s[a] < s[b];
            });
        rk[sa[0]] = 0;
        for (int i = 1; i < n; i++) {
            rk[sa[i]] = rk[sa[i - 1]] + (s[sa[i]] != s[sa[i - 1]]);
        }
        int k = 1;
        std::vector<int> tmp, cnt(n);
        tmp.reserve(n);
        while (rk[sa[n - 1]] < n - 1) {
            tmp.clear();
            for (int i = 0; i < k; i++) {
                tmp.push_back(n - k + i);
            }
            for (auto i : sa) {
                if (i >= k) {
                    tmp.push_back(i - k);
                }
            }
            std::fill(cnt.begin(), cnt.end(), 0);
            for (int i = 0; i < n; i++) {
                cnt[rk[i]]++;
            }
            for (int i = 1; i < n; i++) {
                cnt[i] += cnt[i - 1];
            }
            for (int i = n - 1; i >= 0; i--) {
                sa[--cnt[rk[tmp[i]]]] = tmp[i];
            }
            std::swap(rk, tmp);
            rk[sa[0]] = 0;
            for (int i = 1; i < n; i++) {
                rk[sa[i]] = rk[sa[i - 1]] + (tmp[sa[i - 1]] < tmp[sa[i]] || sa[i - 1] + k == n || tmp[sa[i - 1] + k] < tmp[sa[i] + k]);
            }
            k *= 2;
        }
        for (int i = 0, j = 0; i < n; i++) {
            if (rk[i] == 0) {
                j = 0;
            } else {
                for (j -= j > 0; i + j < n && sa[rk[i] - 1] + j < n && s[i + j] == s[sa[rk[i] - 1] + j]; ) {
                    j++;
                }
                lc[rk[i] - 1] = j;
            }
        }
    }
};

void solve() {
    int n, k;
    std::cin >> n >> k;

    std::string s;
    std::cin >> s;

    SA sa(s + std::string(s.rbegin(), s.rend()));

    int m = sa.lc.size();
    int lgm = std::__lg(m);

    std::vector st(lgm + 1, std::vector<int>(m));
    st[0] = sa.lc;
    for (int j = 0; j < lgm; j++) {
        for (int i = 0; i + (2 << j) <= m; i++) {
            st[j + 1][i] = std::min(st[j][i], st[j][i + (1 << j)]);
        }
    }

    auto rmq = [&](int l, int r) {
        int k = std::__lg(r - l);
        return std::min(st[k][l], st[k][r - (1 << k)]);
    };

    auto get = [&](int i, int j) {
        if (i == 0 || j == n) {
            return 0;
        }
        int x = sa.rk[j], y = sa.rk[n + n - i];
        if (x > y) {
            std::swap(x, y);
        }
        return std::min({n - j, i, rmq(x, y)});
    };

    auto work = [&](int l, int r) {
        int len = get(l, r);
        l -= len;
        r += len;

        int res = r - l;
        for (int i = 1; i <= k; i++) {
            if (l >= i) {
                int L = l - i, R = r;
                len = get(L, R);
                L -= len;
                R += len;
                res = std::max(res, R - L + i);
            }
            if (r + i <= n) {
                int L = l, R = r + i;
                len = get(L, R);
                L -= len;
                R += len;
                res = std::max(res, R - L + i);
            }
        }
        return res;
    };

    auto work2 = [&](int i) {
        int l = i, r = i;
        int res = 0;
        for (int i = 0; i <= k; i++) {
            if (l >= i) {
                int L = l - i, R = r;
                int len = get(L, R);
                L -= len;
                R += len;
                res = std::max(res, R - L + k);
            }
            if (r + i <= n) {
                int L = l, R = r + i;
                int len = get(L, R);
                L -= len;
                R += len;
                res = std::max(res, R - L + k);
            }
        }
        return res;
    };

    int ans = 0;
    for (int i = 0; i < n; i++) {
        ans = std::max(ans, work(i, i));
        ans = std::max(ans, work(i, i + 1));
    }
    for (int i = 0; i <= n; i++) {
        ans = std::max(ans, work2(i));
    }
    std::cout << ans << "\n";
}

int main() {
    std::ios::sync_with_stdio(false);
    std::cin.tie(nullptr);

    int t;
    std::cin >> t;

    while (t--) {
        solve();
    }

    return 0;
}