CIA headquarter collects data from across the country through its classified network. They have been using optical fibres long before it's been deployed on any civilian projects. However they are still under a lot pressure recently because the data are growing rapidly. As a result they are considering upgrading the network with new technologies that provide a few times wider bandwidth. In the experiemental stage, they would like to upgrade one segment of their original network in order to see how it performs. And as a CIA intern it's your responsibility to investigate which segment could actually help increase the total bandwidth the headquarter receives, suppose that all the cities have infinite data to send and the routing algorithm is optimized. As they have prepared the data for you in a few minutes, you are told that they need the result immediately. Well, practically immediately.

Input contains multiple test cases. First line of each test case contains three integers n, m and l, they represent the number of cities, the number of relay stations and the number of segments. Cities will be referred to as integers from 1 to n, while relay stations use integers from n+1 to n+m. You can saves assume that n + m <= 100, l <= 1000 (all of them are positive). The headquarter is identified by the integer 0.

The next l lines hold a segment on each line in the form of a b c, where a is the source node and b is the target node, while c is its bandwidth. They are all integers where a and b are valid identifiers (from 0 to n+m). c is positive. For some reason the data links are all directional.

The input is terminated by a test case with n = 0. You can safely assume that your calculation can be housed within 32-bit integers.

For each test print the segment id's that meets the criteria. The result is printed in a single line and sorted in ascending order, with a single space as the separator. If none of the segment meets the criteria, just print an empty line. The segment id is 1 based not 0 based.

 #include <cstdio>

 #include <cstring>

 #include <algorithm>

 #include <queue>

 using namespace std;

 const int MAXN = ;

 const int MAXE = ;

 const int INF = 0x3fff3fff;

 struct SAP {

     int head[MAXN], dis[MAXN], pre[MAXN], cur[MAXN], gap[MAXN];

     int to[MAXE], next[MAXE], flow[MAXE];

     int n, st, ed, ecnt;

     void init() {

         memset(head, , sizeof(head));

         ecnt = ;

     }

     void add_edge(int u, int v, int c) {

         to[ecnt] = v; flow[ecnt] = c; next[ecnt] = head[u]; head[u] = ecnt++;

         to[ecnt] = u; flow[ecnt] = ; next[ecnt] = head[v]; head[v] = ecnt++;

         //printf("%d->%d flow = %d\n", u, v, c);

     }

     void bfs() {

         memset(dis, 0x3f, sizeof(dis));

         queue<int> que; que.push(ed);

         dis[ed] = ;

         while(!que.empty()) {

             int u = que.front(); que.pop();

             ++gap[dis[u]];

             for(int p = head[u]; p; p = next[p]) {

                 int &v = to[p];

                 if(flow[p ^ ] && dis[v] > n) {

                     dis[v] = dis[u] + ;

                     que.push(v);

                 }

             }

         }

     }

     int Max_flow(int ss, int tt, int nn) {

         st = ss; ed = tt; n = nn;

         int ans = , minFlow = INF, u;

         for(int i = ; i <= n; ++i) {

             cur[i] = head[i];

             gap[i] = ;

         }

         u = pre[st] = st;

         bfs();

         while(dis[st] < n) {

             bool flag = false;

             for(int &p = cur[u]; p; p = next[p]) {

                 int &v = to[p];

                 if(flow[p] && dis[u] == dis[v] + ) {

                     flag = true;

                     minFlow = min(minFlow, flow[p]);

                     pre[v] = u;

                     u = v;

                     if(u == ed) {

                         ans += minFlow;

                         while(u != st) {

                             u = pre[u];

                             flow[cur[u]] -= minFlow;

                             flow[cur[u] ^ ] += minFlow;

                         }

                         minFlow = INF;

                     }

                     break;

                 }

             }

             if(flag) continue;

             int minDis = n - ;

             for(int p = head[u]; p; p = next[p]) {

                 int &v = to[p];

                 if(flow[p] && minDis > dis[v]) {

                     minDis = dis[v];

                     cur[u] = p;

                 }

             }

             if(--gap[dis[u]] == ) break;

             gap[dis[u] = minDis + ]++;

             u = pre[u];

         }

         return ans;

     }

     int mark[MAXN];

     void make_cut() {

         memset(mark, , sizeof(mark));

         queue<int> que;

         que.push(st); mark[st] = ;

         while(!que.empty()) {

             int u = que.front(); que.pop();

             for(int p = head[u]; p; p = next[p]) {

                 int &v = to[p];

                 if(flow[p] && !mark[v]) {

                     mark[v] = ;

                     que.push(v);

                 }

             }

         }

         que.push(ed); mark[ed] = ;

         while(!que.empty()) {

             int u = que.front(); que.pop();

             for(int p = head[u]; p; p = next[p]) {

                 int &v = to[p];

                 if(flow[p ^ ] && !mark[v]) {

                     mark[v] = ;

                     que.push(v);

                 }

             }

         }

     }

 } G;

 int from[MAXE], to[MAXE];

 int n, m, L, c;

 int main() {

     while(scanf("%d%d%d", &n, &m, &L) != EOF) {

         if(n == ) break;

         int ss = n + m + , tt = ;

         G.init();

         for(int i = ; i <= n; ++i) G.add_edge(ss, i, INF);

         for(int i = ; i <= L; ++i) {

             scanf("%d%d%d", &from[i], &to[i], &c);

             G.add_edge(from[i], to[i], c);

         }

         //printf("%d\n", G.Max_flow(ss, tt, ss));

         G.Max_flow(ss, tt, ss);

         G.make_cut();

         bool flag = false;

         for(int i = ; i <= L; ++i) {

             int &u = from[i], &v = to[i];

             if(G.mark[u] ==  && G.mark[v] == ) {

                 if(flag) printf(" ");

                 printf("%d", i);

                 flag = true;

             }

         }

         puts("");

     }

 }