1
  2
  3
  4
  5
  6
  7
  8
  9
 10
 11
 12
 13
 14
 15
 16
 17
 18
 19
 20
 21
 22
 23
 24
 25
 26
 27
 28
 29
 30
 31
 32
 33
 34
 35
 36
 37
 38
 39
 40
 41
 42
 43
 44
 45
 46
 47
 48
 49
 50
 51
 52
 53
 54
 55
 56
 57
 58
 59
 60
 61
 62
 63
 64
 65
 66
 67
 68
 69
 70
 71
 72
 73
 74
 75
 76
 77
 78
 79
 80
 81
 82
 83
 84
 85
 86
 87
 88
 89
 90
 91
 92
 93
 94
 95
 96
 97
 98
 99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
#include <iostream>
#include <unordered_map>
#include <vector>

int64_t resolve_cycles(int64_t w, const std::vector<std::pair<int64_t, int64_t>> &cycles, int32_t i) {
    // std::cerr << std::string(i, ' ') << "resolve (" << w << " " << cycles[i].first << " " << cycles[i].second << ")\n";
    if (i + 1 == cycles.size()) {
        while (w * cycles[i].first <= cycles[i].second) {
            w *= cycles[i].first;
        }
        // std::cerr << std::string(i, ' ') << "= " << w << "\n";
        return w;
    }

    int64_t best = resolve_cycles(w, cycles, i + 1);
    while (w * cycles[i].first <= cycles[i].second) {
        w *= cycles[i].first;
        best = std::max(best, resolve_cycles(w, cycles, i + 1));
    }
    // std::cerr << std::string(i, ' ') << "= " << best << "\n";
    return best;
}

void collect_cycles(int32_t n, int32_t m, const std::vector<int64_t> &p, const std::unordered_multimap<int32_t, std::pair<int32_t, int64_t>> &x, std::vector<int32_t> &seen_i, std::vector<int64_t> &seen_w, std::vector<int32_t> &path, std::unordered_multimap<int32_t, std::pair<int64_t, int64_t>> &all_cycles, int32_t cur_i, int64_t cur_w) {
    if (cur_w > p[cur_i]) {
        return;
    }
    seen_i[cur_i] = path.size();
    seen_w[cur_i] = cur_w;
    path.push_back(cur_i);

    auto range = x.equal_range(cur_i);
    for (auto it = range.first; it != range.second; ++it) {
        auto val = it->second;
        if (seen_i[val.first] == -1) {
            continue;
        }
        // std::cerr << "cycle: " << cur_i << " -> " << val.first << "\n";
        int64_t mult = val.second;
        int64_t max = p[val.first];
        for (int32_t i = seen_i[val.first]; i + 1 < path.size(); ++i) {
            int32_t from = path[i];
            int32_t to = path[i + 1];
            // std::cerr << " segment: " << seen_w[to] << " / " << seen_w[from] << "\n";
            int64_t m1 = seen_w[to] / seen_w[from];
            mult *= m1;
            max *= m1;
            max = std::min(max, p[to]);
            if (mult > max) {
                goto skip;
            }
        }
        // std::cerr << " is: " << mult << " " << max << "\n";
        if (mult > 1) {
            all_cycles.insert({val.first, {mult, max}});
        }
        skip:;
    }

    for (auto it = range.first; it != range.second; ++it) {
        auto val = it->second;
        if (seen_i[val.first] != -1) {
            continue;
        }
        collect_cycles(n, m, p, x, seen_i, seen_w, path, all_cycles, val.first, cur_w * val.second);
    }

    seen_i[cur_i] = -1;
    path.pop_back();
}

int64_t goo(int32_t n, int32_t m, const std::vector<int64_t> &p, const std::unordered_multimap<int32_t, std::pair<int32_t, int64_t>> &x, std::vector<int32_t> &seen_i, std::vector<int64_t> &seen_w, std::vector<int32_t> &path, const std::unordered_multimap<int32_t, std::pair<int64_t, int64_t>> &all_cycles, std::vector<std::pair<int64_t, int64_t>> &path_cycles, int32_t cur_i, int64_t cur_w) {
    if (cur_w > p[cur_i]) {
        return -1;
    }
    seen_i[cur_i] = path.size();
    seen_w[cur_i] = cur_w;
    path.push_back(cur_i);

    // std::cerr << "goo at " << cur_i << "\n";
    for (auto &c: path_cycles) {
        c.second = std::min(c.second, p[cur_i]);
        // std::cerr << " have cycle " << c.first << " " << c.second << "\n";
    }

    int32_t cycles_to_drop = 0;
    auto range1 = all_cycles.equal_range(cur_i);
    for (auto it = range1.first; it != range1.second; ++it) {
        path_cycles.push_back(it->second);
        // std::cerr << " have cycle " << path_cycles.back().first << " " << path_cycles.back().second << "\n";
        cycles_to_drop += 1;
    }

    int64_t best = -1;
    if (cur_i == n - 1) {
        best = path_cycles.empty() ? cur_w : resolve_cycles(cur_w, path_cycles, 0);
    } else {
        auto range = x.equal_range(cur_i);
        for (auto it = range.first; it != range.second; ++it) {
            auto val = it->second;
            if (seen_i[val.first] != -1) {
                continue;
            }
            for (auto &c: path_cycles) {
                c.second *= val.second;
            }
            best = std::max(best, goo(n, m, p, x, seen_i, seen_w, path, all_cycles, path_cycles, val.first, cur_w * val.second));
            for (auto &c: path_cycles) {
                c.second /= val.second;
            }
        }
    }

    for (int32_t i = 0; i < cycles_to_drop; ++i) {
        path_cycles.pop_back();
    }
    seen_i[cur_i] = -1;
    path.pop_back();
    return best;
}

void go() {
    int32_t n, m;
    std::cin >> n >> m;

    std::vector<int64_t> p(n);
    for (int32_t i = 0; i < n; ++i) {
        std::cin >> p[i];
    }

    std::unordered_multimap<int32_t, std::pair<int32_t, int64_t>> x;
    for (int32_t i = 0; i < m; ++i) {
        int32_t a, b;
        int64_t w;
        std::cin >> a >> b >> w;
        x.insert({a - 1, {b - 1, w}});
    }

    std::vector<int32_t> seen_i(n, -1);
    std::vector<int64_t> seen_w(n, -1);
    std::vector<int32_t> path;
    std::unordered_multimap<int32_t, std::pair<int64_t, int64_t>> all_cycles;
    std::vector<std::pair<int64_t, int64_t>> path_cycles;

    collect_cycles(n, m, p, x, seen_i, seen_w, path, all_cycles, 0, 1);
    std::cout << goo(n, m, p, x, seen_i, seen_w, path, all_cycles, path_cycles, 0, 1) << "\n";
}

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

    int32_t t;
    std::cin >> t;

    for (int32_t i = 0; i < t; ++i) {
        go();
    }
}