#include <bits/stdc++.h>

#define long long long int
#define DEBUG
using namespace std;

// @author: pashka

struct test {

    struct seg {
        int r;
        int ans = INT_MAX;
        int p = -1;
    };

    int find(vector<seg> &a, int x) {
        int l = -1;
        int r = (int) a.size();
        while (r > l + 1) {
            int m = (l + r) / 2;
            if (a[m].r < x) l = m; else r = m;
        }
        return r;
    }

    void solve() {
        int n, m;
        cin >> m >> n;
        vector<int> c(m);
        for (int i = 0; i < m; i++) cin >> c[i];
        vector<vector<int>> a(n, vector<int>(m));
        for (int i = 0; i < n; i++) {
            for (int j = 0; j < m; j++) {
                cin >> a[i][j];
            }
        }
        for (int i = 0; i < m; i++)
            if (c[i] == 1 && a[0][i] > 0) {
                cout << "-1\n";
                return;
            }
        for (int i = 0; i < n; i++) {
            bool ok = false;
            for (int j = 0; j < m; j++) {
                if (a[i][j] == 0)ok = true;
            }
            if (!ok) {
                cout << "-1\n";
                return;
            }
        }
        vector<vector<vector<seg>>> s(n, vector<vector<seg>>(m));
        for (int i = 0; i < n; i++) {
            for (int j = 0; j < m; j++) {
                if (a[i][j] == 0) {
                    for (int k = j; k < m; k++) {
                        if (k != j && a[i][k] == 0) break;
                        s[i][j].push_back({k, INT_MAX, -1});
                    }
                } else {
                    int k = j + 1;
                    while (k < m && a[i][k] != 0) k++;
                    if (k < m) {
                        s[i][j].push_back({k, INT_MAX, -1});
                    }
                }
            }
        }
        vector<int> p(n, m);
        for (int j = m - 1; j >= 0; j--) {
            for (int i = 0; i < n; i++) {
                if (a[i][j] == 0) p[i] = j;
            }
            vector<int> st;
            for (int i = 0; i < n; i++) {
                while (!st.empty() && p[st.back()] < p[i]) st.pop_back();
                for (auto &ss: s[i][j]) {
                    int l = -1;
                    int r = (int) st.size();
                    while (r > l + 1) {
                        int mm = (l + r) / 2;
                        if (p[st[mm]] > ss.r) {
                            l = mm;
                        } else {
                            r = mm;
                        }
                    }
                    if (l != -1) {
                        ss.p = st[l];
                    }
                }
                st.push_back(i);
            }
        }
        vector<vector<int>> ps(n, vector<int>(m + 1));
        for (int i = 0; i < n; i++) {
            for (int j = 0; j < m; j++) {
                ps[i][j + 1] = ps[i][j] + a[i][j];
            }
        }
        for (int i = 1; i < n; i++) {
            for (int j = 0; j <= m; j++) {
                ps[i][j] += ps[i - 1][j];
            }
        }
        vector<vector<int>> nr(n, vector<int>(m));
        vector<vector<int>> nl(n, vector<int>(m));
        for (int i = 0; i < n; i++) {
            int k = -1;
            for (int j = 0; j < m; j++) {
                if (a[i][j] == 0) k = j;
                nl[i][j] = k;
            }
            k = m;
            for (int j = m - 1; j >= 0; j--) {
                if (a[i][j] == 0) k = j;
                nr[i][j] = k;
            }
        }

        for (int j = 0; j < m; j++) {
            for (auto &ss: s[n - 1][j]) {
                ss.ans = ps[n - 1][ss.r + 1] - ps[n - 1][j];
            }
        }

        for (int i = n - 1; i >= 0; i--) {
            for (int j = 0; j < m; j++) {
                for (auto &ss: s[i][j]) {
                    if (ss.ans == INT_MAX) continue;
                    if (ss.p == -1) continue;
                    int l = j;
                    int r = ss.r;
                    int ii = ss.p;
                    int rr = nr[ii][r];
                    if (rr < m) {
                        auto &ss2 = s[ii][l][find(s[ii][l], rr)];
                        ss2.ans = min(ss2.ans, ss.ans +
                                               ps[ii][rr + 1] - ps[ii][r + 1]
                        );
                    }
                    int ll = nl[ii][l];
                    if (ll >= 0) {
                        auto &ss2 = s[ii][ll][find(s[ii][ll], r)];
                        ss2.ans = min(ss2.ans, ss.ans +
                                               ps[ii][l] - ps[ii][ll]
                        );
                    }
                }
            }
        }

//        for (int i = 0; i < n; i++) {
//            for (int j = 0; j < m; j++) {
//                for (auto &ss : s[i][j]) {
//                    cout << i << " " << j << "-" << ss.r << ": " << ss.ans << " ^ " << ss.p << "\n";
//                }
//            }
//        }

        vector<long> d1(m + 1, INT_MAX);
        vector<long> d2(m + 1, INT_MAX);
        vector<long> d3(m + 1, INT_MAX);
        d1[0] = 0;
        for (int j = 0; j < m; j++) {
            if (c[j] == 0) {
                d1[j + 1] = min(d1[j + 1], min(d1[j], d3[j]));
            }

            d2[j + 1] = min(d2[j + 1], min(d1[j], d2[j]) + a[0][j]);

            d3[j + 1] = min(d3[j + 1], d3[j] + a[0][j]);
            for (int i = 0; i < n; i++) {
                for (auto &ss: s[i][j]) {
                    if (ss.ans == INT_MAX) continue;
                    d3[ss.r + 1] = min(
                            d3[ss.r + 1],
                            min(d1[j], d2[j]) + ss.ans
                            );
                }
            }
        }
        cout << min(d1[m], d3[m]) << "\n";
    }
};

int main() {
    ios::sync_with_stdio(false);

    int n;
    cin >> n;
    for (int i = 0; i < n; i++) {
        test().solve();
    }

    return 0;
}