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/*
>>~~ UVa Online Judge ACM Problem Solution ~~<<
ID: 10044
Name: Erdos Numbers
Problem: https://onlinejudge.org/external/100/10044.pdf
Language: C++
Author: Arash Shakery
Email: [email protected]
*/
#include <stdio.h>
#include <cstring>
#include <iostream>
#include <string>
#include <vector>
#include <map>
using namespace std;
#define INF 536870912
#define MAXN 5001
#define MAXL 20000
int graph[MAXN][MAXN], adj[MAXN][MAXN], deg[MAXN];
int d[MAXN], q[MAXN], inq[MAXN], qs;
#define CLR( x, v ) memset( x, v, sizeof( x ) )
#define BUBL { \
t = q[i]; q[i] = q[j]; q[j] = t; \
t = inq[q[i]]; inq[q[i]] = inq[q[j]]; inq[q[j]] = t; }
int dijkstra( int n, int s, int t ) {
CLR( d, 9 ); CLR( inq, -1 );
d[s] = qs = 0;
inq[q[qs++] = s] = 0;
while( qs ) {
// get the minimum from the q
int u = q[0]; inq[u] = -1;
// bubble down
q[0] = q[--qs];
if( qs ) inq[q[0]] = 0;
for( int i = 0, j = 2*i + 1, t; j < qs; i = j, j = 2*i + 1 ) {
if( j + 1 < qs && d[q[j + 1]] < d[q[j]] ) j++;
if( d[q[j]] >= d[q[i]] ) break;
BUBL;
}
// relax neighbours
for( int k = 0, v = adj[u][k]; k < deg[u]; v = adj[u][++k] ) {
int newd = d[u] + graph[u][v];
if( newd < d[v] ) {
d[v] = newd;
if( inq[v] < 0 ) { inq[q[qs] = v] = qs; qs++; }
// bubble up
for( int i = inq[v], j = ( i - 1 )/2, t;
d[q[i]] < d[q[j]]; i = j, j = ( i - 1 )/2 )
BUBL;
}
}
}
return d[t];
}
char line[MAXL];
int ex[MAXN*MAXN],
ey[MAXN*MAXN];
int main(){
int T, p, n;
cin>>T;
for(int cse=1; cse<=T; cse++) {
int cnt = 0, ec = 0;
map<string, int> ids;
ids["Erdos, P."] = cnt++;
cin>>p>>n;
while(getchar()!='\n');
for (int i=0; i<p; i++) {
cin.getline(line, MAXL);
char *e = strchr(line, ':');
e[0] = 0;
vector<int> cur;
string name;
bool ff = false;
for (char* s=strtok(line, " ,"); s; s=strtok(NULL, " ,")) {
if (ff) {
ff = false;
name = name + ", " + s;
int id = 0;
if (name != "Erdos, P.") {
id = ids[name];
if (id == 0)
id = ids[name] = cnt++;
}
for (int j=cur.size()-1; j>=0; j--) {
int k = cur[j];
if (k!=id) {
ex[ec] = k;
ey[ec++] = id;
}
}
cur.push_back(id);
}
else {
ff = true;
name = s;
}
}
}
for (int i=0; i<cnt; i++) {
deg[i] = 0;
for (int j=i+1; j<cnt; j++)
graph[i][j] = graph[j][i] = INF;
}
for (int k=0; k<ec; k++) {
int i = ex[k], j = ey[k];
graph[i][j] = graph[j][i] = 1;
adj[i][deg[i]++] = j;
adj[j][deg[j]++] = i;
}
printf("Scenario %d\n", cse);
for (int i=0; i<n; i++) {
cin.getline(line, MAXL);
auto it = ids.find(line);
int res = (it == ids.end()) ? INF : dijkstra(cnt, 0, it->second);
cout << line << " ";
if (res >= cnt) cout << "infinity\n";
else cout << res << endl;
}
}
}
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