#include<iostream>
#include<vector>
#include<cassert>

#include <algorithm>
#include <cassert>
#include <numeric>
#include <string>
#include <vector>

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;
}

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);
}

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);
}

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

using namespace std;
//Disjoint Sparse Table
struct DST{
	int n;
	vector<vector<int> >dat;
	DST(const vector<int>&v={})
	{
		n=v.size();
		dat.push_back(v);
		for(int i=2;i<n;i<<=1)
		{
			dat.push_back(vector<int>(n));
			for(int j=i;j<n;j+=i<<1)
			{
				dat.back()[j-1]=dat[0][j-1];
				for(int k=2;k<=i;k++)
				{
					dat.back()[j-k]=min(dat[0][j-k],dat.back()[j-k+1]);
				}
				dat.back()[j]=dat[0][j];
				for(int k=2;k<=i&&j+k<=n;k++)
				{
					dat.back()[j+k-1]=min(dat.back()[j+k-2],dat[0][j+k-1]);
				}
			}
		}
	}
	int query(int l,int r)const//[l,r)
	{
		if(l<0)l=0;
		if(r>n)r=n;
		r--;
		if(l==r)return dat[0][l];
		int k=31-__builtin_clz(l^r);
		return min(dat[k][l],dat[k][r]);
	}
};
DST dst;
int inv[4<<17];
int main()
{
	ios::sync_with_stdio(false);
	cin.tie(nullptr);
	int T;cin>>T;
	for(;T--;)
	{
		int N,K;
		string S;
		cin>>N>>K>>S;
		{
			string rS=S;
			reverse(rS.begin(),rS.end());
			string T=S+rS;
			vector<int>sa=atcoder::suffix_array(T);
			vector<int>lcp=atcoder::lcp_array(T,sa);
			inv[N+N]=0;
			for(int i=0;i<sa.size();i++)inv[sa[i]]=i+1;
			lcp.insert(lcp.begin(),0);
			dst=DST(lcp);
		}
		auto lcp=[&N](int lft,int rgt){
			assert(0<=lft&&lft<=N);
			assert(0<=rgt&&rgt<=N);
			int x=inv[N+N-lft],y=inv[rgt];
			if(x>y)swap(x,y);
			if(x==y)return 0;
			int len=dst.query(x,y);
			return min(len,min(lft,N-rgt));
		};
		int ans=0;
		for(int i=0;i<=N;i++)
		{
			if(i<N)
			{//odd
				int len=lcp(i,i+1);
				{//add left
					for(int a=1;a<=K&&i+1+len+a<=N;a++)
					{
						int addlen=lcp(i-len,i+1+len+a);
						ans=max(ans,(len+a+addlen)*2+1);
					}
				}
				{//add right
					for(int a=1;a<=K&&i-len-a>=0;a++)
					{
						int addlen=lcp(i-len-a,i+1+len);
						ans=max(ans,(len+a+addlen)*2+1);
					}
				}
			}
			{//even
				int len=lcp(i,i);
				{//add left
					for(int a=1;a<=K&&i+len+a<=N;a++)
					{
						int addlen=lcp(i-len,i+len+a);
						ans=max(ans,(len+a+addlen)*2);
					}
				}
				{//add right
					for(int a=1;a<=K&&i-len-a>=0;a++)
					{
						int addlen=lcp(i-len-a,i+len);
						ans=max(ans,(len+a+addlen)*2);
					}
				}
				ans=max(ans,K+len*2);
			}
			{//mid
				for(int a=1;a<=K;a++)
				{
					if(a<=i)
					{
						int len=lcp(i-a,i);
						ans=max(ans,a+K+len*2);
					}
					if(i+a<=N)
					{
						int len=lcp(i,i+a);
						ans=max(ans,a+K+len*2);
					}
				}
			}
		}
		cout<<ans<<"\n";
	}
}