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
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
#include <iostream>
#include <vector>
#include <string>

using namespace std;

const int INF = 1e9;

void send_bit(int b) {
    cout << "+ " << b << "\n";
    cout.flush();
}

int receive_bit() {
    cout << "?\n";
    cout.flush();
    char c;
    cin >> c;
    return c - '0';
}

int bits_needed(int u) {
    if (u <= 1) return 0;
    int b = 0;
    while ((1 << b) < u) b++;
    return b;
}

struct Edge {
    int to;
    int weight;
};

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

    string role;
    if (!(cin >> role)) return 0;
    bool is_algosia = (role == "Algosia");

    int n, m;
    cin >> n >> m;

    vector<vector<Edge>> adj(n + 1);
    for (int i = 0; i < m; ++i) {
        int u, v, c;
        cin >> u >> v >> c;
        adj[u].push_back({v, c});
        adj[v].push_back({u, c});
    }

    vector<int> dist(n + 1, INF);
    vector<bool> visited(n + 1, false);

    dist[1] = 0;
    visited[1] = true;
    int last_d = 0;

    vector<int> unvisited;
    for (int i = 2; i <= n; ++i) {
        unvisited.push_back(i);
    }

    for (auto edge : adj[1]) {
        if (dist[edge.to] > dist[1] + edge.weight) {
            dist[edge.to] = dist[1] + edge.weight;
        }
    }

    for (int step = 0; step < n - 1; ++step) {
        int U = unvisited.size();
        int min_d = INF;
        int min_u = -1;

        for (int u : unvisited) {
            if (dist[u] < min_d) {
                min_d = dist[u];
                min_u = u;
            }
        }

        int delta = (min_d == INF) ? 511 : (min_d - last_d);
        
        int delta_A = is_algosia ? delta : 0;
        int delta_B = !is_algosia ? delta : 0;

        int winner = -1;
        int k_mismatch = -1;

        for (int k = 8; k >= 0; --k) {
            int bit_A = is_algosia ? ((delta_A >> k) & 1) : 0;
            int bit_B = !is_algosia ? ((delta_B >> k) & 1) : 0;
            
            if (is_algosia) send_bit(bit_A);
            int recv_A = is_algosia ? bit_A : receive_bit();
            
            int match = (!is_algosia) ? (bit_B == recv_A ? 0 : 1) : 0;
            if (!is_algosia) send_bit(match);
            int recv_match = is_algosia ? receive_bit() : match;
            
            if (recv_match == 1) {
                if (recv_A == 0) winner = 0;
                else winner = 1;
                k_mismatch = k;
                break;
            }
        }

        if (winner == -1) winner = 2;

        int final_delta = 0;
        for (int k = 8; k > k_mismatch; --k) {
            if ((delta >> k) & 1) final_delta |= (1 << k);
        }

        if (winner == 0) {
            for (int k = k_mismatch - 1; k >= 0; --k) {
                if (is_algosia) send_bit((delta >> k) & 1);
                int b = is_algosia ? ((delta >> k) & 1) : receive_bit();
                if (b) final_delta |= (1 << k);
            }
        } else if (winner == 1) {
            for (int k = k_mismatch - 1; k >= 0; --k) {
                if (!is_algosia) send_bit((delta >> k) & 1);
                int b = is_algosia ? receive_bit() : ((delta >> k) & 1);
                if (b) final_delta |= (1 << k);
            }
        } else {
            final_delta = delta;
        }

        int num_bits_u = bits_needed(U);
        int final_u_idx = 0;

        if (winner == 0 || winner == 2) {
            int u_idx = -1;
            if (is_algosia) {
                for (int i = 0; i < U; ++i) {
                    if (unvisited[i] == min_u) {
                        u_idx = i;
                        break;
                    }
                }
            }
            for (int k = num_bits_u - 1; k >= 0; --k) {
                if (is_algosia) send_bit((u_idx >> k) & 1);
                int b = is_algosia ? ((u_idx >> k) & 1) : receive_bit();
                if (b) final_u_idx |= (1 << k);
            }
        } else {
            int u_idx = -1;
            if (!is_algosia) {
                for (int i = 0; i < U; ++i) {
                    if (unvisited[i] == min_u) {
                        u_idx = i;
                        break;
                    }
                }
            }
            for (int k = num_bits_u - 1; k >= 0; --k) {
                if (!is_algosia) send_bit((u_idx >> k) & 1);
                int b = is_algosia ? receive_bit() : ((u_idx >> k) & 1);
                if (b) final_u_idx |= (1 << k);
            }
        }

        int final_u = unvisited[final_u_idx];
        unvisited.erase(unvisited.begin() + final_u_idx);
        
        last_d += final_delta;
        visited[final_u] = true;
        dist[final_u] = last_d;

        for (auto edge : adj[final_u]) {
            if (!visited[edge.to] && dist[edge.to] > dist[final_u] + edge.weight) {
                dist[edge.to] = dist[final_u] + edge.weight;
            }
        }
    }

    if (is_algosia) {
        cout << "!";
        for (int i = 1; i <= n; ++i) {
            cout << " " << dist[i];
        }
        cout << "\n";
        cout.flush();
    }

    return 0;
}