#ifdef DEBUG
#define _GLIBCXX_DEBUG
#endif
//#pragma GCC optimize("O3")
#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef long double ld;
struct pt{
    ll x, y;
};
int n, k;
const int maxN = 2e5 + 10;
pt a[maxN];
bool isCcw(pt a, pt b, pt c) {
    return (b.x - a.x) * (c.y - a.y) > (b.y - a.y) * (c.x - a.x);
}
bool isCw(pt a, pt b, pt c) {
    return (b.x - a.x) * (c.y - a.y) < (b.y - a.y) * (c.x - a.x);
}
ll area(pt a, pt b, pt c) {
    return (b.x - a.x) * (c.y - a.y) - (b.y - a.y) * (c.x - a.x);
}
vector<pt> convexHull(vector<pt> pts) {
    if (pts.size() < 3) {
        return pts;
    }
    sort(pts.begin(), pts.end(), [&](const pt &a, const pt &b) {
        return make_pair(a.x, a.y) < make_pair(b.x, b.y);
    });
    pt pUp = pts.front(), pDown = pts.back();
    vector<pt> up{pUp}, down{pUp};
    for (size_t i = 1; i < pts.size(); ++i) {
        if (i == pts.size() - 1 || area(pUp, pts[i], pDown) < 0) {
            while (up.size() >= 2 &&
                   area(up[up.size()-2], up.back(), pts[i]) >= 0) {
                up.pop_back();
            }
            up.push_back(pts[i]);
        }
        if (i == pts.size() - 1 || area(pUp, pts[i], pDown) > 0) {
            while (down.size() >= 2 &&
                   area(down[down.size()-2], down.back(), pts[i]) <= 0) {
                down.pop_back();
            }
            down.push_back(pts[i]);
        }
    }
    assert(up.size() >= 2);
    for (size_t i = up.size() - 2; i > 0; --i) {
        down.push_back(up[i]);
    }
    return down;
}
ld len(pt a, pt b) {
    return sqrtl((a.x - b.x) * (a.x - b.x) + (a.y - b.y) * (a.y - b.y));
}
int tp(pt A) {
    if (A.y > 0 || (A.y == 0 && A.x > 0)) return -1;
    return 1;
}
bool cmp(const pt& A, const pt& B) {
    if (tp(A) != tp(B)) return tp(A) < tp(B);
    if (A.x * B.y != A.y * B.x) return A.x * B.y > A.y * B.x;
    return (A.x * A.x + A.y * A.y < B.x * B.x + B.y * B.y);
}
void solve() {
    cin >> n >> k;
    vector<pt> T;
    for (int i = 1; i <= n; i++) {
        cin >> a[i].x >> a[i].y;
    }
    pt ini = a[k];
    for (int i = 1; i <= n; i++) {
        a[i].x -= ini.x;
        a[i].y -= ini.y;
        T.emplace_back(a[i]);
    }
    ini.x = 0;
    ini.y = 0;
    auto ch = convexHull(T);
    assert(ch.size() >= 3);
    ld cur = 0;
    for (int z = 0; z < ch.size(); z++) {
        cur += len(ch[z], ch[(z + 1) % ch.size()]);
    }
    for (int z = 1; z + 1 < ch.size(); z++) {
        assert(area(ch[0], ch[z], ch[z + 1]) > 0);
    }
//    for (auto& it :ch) {
//        cout << it.x << " " << it.y << endl;
//    }
    for (int z = 0; z < ch.size(); z++) {
        if (area(ch[z], ch[(z + 1) % ch.size()], ini) == 0) {
            cout << fixed << setprecision(3) << cur << '\n';
            return;
        }
    }
    vector<pt> S;
    for (int i = 1; i <= n; i++) {
        if (i == k) continue;
        S.emplace_back(a[i]);
    }
    sort(S.begin(), S.end(), cmp);
    vector<pt> nS;
    for (int z = 0; z < S.size(); z++) {
        if (z + 1 < S.size() && tp(S[z]) == tp(S[z + 1]) && S[z].x * S[z + 1].y == S[z].y * S[z + 1].x) {

        }
        else {
            nS.push_back(S[z]);
        }
    }
    S = nS;
    //S -- good
    ld best = 1e18;
    for (int t = 0; t < ch.size(); t++) {
        int l = lower_bound(S.begin(), S.end(), ch[t], cmp) - S.begin();
        int r = lower_bound(S.begin(), S.end(), ch[(t + 1) % ch.size()], cmp) - S.begin();
        assert(S[l].x == ch[t].x && S[l].y == ch[t].y);
        ld cand = cur - len(ch[t], ch[(t + 1) % ch.size()]);
        vector<pt> f;
        for (int z = l; z != r; z = (z + 1) % S.size()) {
            f.emplace_back(S[z]);
        }
        f.emplace_back(S[r]);
        vector<ld> down(f.size()), up(f.size());
        ld cur_s = 0;
        vector<pt> st;
        down[0] = len(ini, f[0]);
        st.push_back(f[0]);
        cur_s = 0;
        for (int i = 0; i + 2 < f.size(); i++) {
            while (st.size() >= 2 && area(f[i + 1], st[st.size() - 1], st[st.size() - 2]) >= 0) {
                cur_s -= len(st[st.size() - 1], st[st.size() - 2]);
                st.pop_back();
            }
            cur_s += len(st[st.size() - 1], f[i + 1]);
            down[i + 1] = cur_s + len(f[i + 1], ini);
            st.push_back(f[i + 1]);
        }
        cur_s = 0;
        st.clear();
        up[f.size() - 1] = len(ini, f.back());
        st.push_back(f.back());
        cur_s = 0;
        for (int i = f.size() - 2; i > 0; i--) {
            while (st.size() >= 2 && area(f[i], st[st.size() - 1], st[st.size() - 2]) <= 0) {
                cur_s -= len(st[st.size() - 1], st[st.size() - 2]);
                st.pop_back();
            }
            cur_s += len(st[st.size() - 1], f[i]);
            up[i] = cur_s + len(f[i], ini);
            st.push_back(f[i]);
        }
        for (int z = 0; z + 1 < f.size(); z++) {
            best = min(best, down[z] + up[z + 1] + cand);
        }
    }
    cout << fixed << setprecision(3) << best << '\n';
}
int main() {
    ios_base::sync_with_stdio(false);
    cin.tie(nullptr);
#ifdef DEBUG
    freopen("input.txt", "r", stdin);
#endif
    int tst;
    cin >> tst;
    while (tst--) {
        solve();
    }
    return 0;
}