#include <bits/stdc++.h>
using namespace std;
class LCT {
public:
static const int MAXN = 100005;
struct Node {
static Node *EMPTY;
Node *ch[2], *fa;
int rev;
int size;
Node() {
ch[0] = ch[1] = fa = NULL;
rev = 0;
size = 1;
}
bool is_root() {
return fa->ch[0] != this && fa->ch[1] != this;
}
void pushdown() {
if (rev) {
ch[0]->rev ^= 1, ch[1]->rev ^= 1;
swap(ch[0], ch[1]);
rev ^= 1;
}
}
void pushup() {
if (this == EMPTY) return ;
size = 1;
if (ch[0] != EMPTY)
size += ch[0]->size;
if (ch[1] != EMPTY)
size += ch[1]->size;
}
} _mem[MAXN];
int bufIdx;
LCT() {
Node::EMPTY = &_mem[0];
Node::EMPTY->fa = Node::EMPTY->ch[0] = Node::EMPTY->ch[1] = Node::EMPTY;
Node::EMPTY->size = 0;
bufIdx = 1;
}
void init() {
bufIdx = 1;
}
Node* newNode() {
Node *u = &_mem[bufIdx++];
*u = Node();
u->fa = u->ch[0] = u->ch[1] = Node::EMPTY;
return u;
}
void rotate(Node *x) {
Node *y;
int d;
y = x->fa, d = y->ch[1] == x ? 1 : 0;
x->ch[d^1]->fa = y, y->ch[d] = x->ch[d^1];
x->ch[d^1] = y;
if (!y->is_root())
y->fa->ch[y->fa->ch[1] == y] = x;
x->fa = y->fa, y->fa = x;
y->pushup(), x->pushup();
}
void deal(Node *x) {
if (!x->is_root()) deal(x->fa);
x->pushdown();
}
void splay(Node *x) {
Node *y, *z;
deal(x);
while (!x->is_root()) {
y = x->fa, z = y->fa;
if (!y->is_root()) {
if (y->ch[0] == x ^ z->ch[0] == y)
rotate(x);
else
rotate(y);
}
rotate(x);
}
x->pushup();
}
Node* access(Node *u) {
Node *v = Node::EMPTY;
for (; u != Node::EMPTY; u = u->fa) {
splay(u);
u->ch[1] = v;
v = u;
v->pushup();
}
return v;
}
void mk_root(Node *u) {
access(u)->rev ^= 1, splay(u);
}
void cut(Node *x, Node *y) {
mk_root(x);
access(y), splay(y);
y->ch[0] = x->fa = Node::EMPTY;
}
Node* cut(Node *x) {
Node *u, *v, *rt = find(x);
mk_root(rt);
access(x), splay(x);
for (v = x->ch[0]; v->ch[1] != Node::EMPTY; v = v->ch[1]);
x->ch[0]->fa = x->fa;
x->fa = x->ch[0] = Node::EMPTY;
return v;
}
void link(Node *x, Node *y) {
mk_root(x);
x->fa = y;
}
Node* find(Node *x) {
for (x = access(x); x->pushdown(), x->ch[0] != Node::EMPTY; x = x->ch[0]);
return x;
}
Node* lca(Node *x, Node *y) {
if (x == y) return x;
if (find(x) != find(y))
return Node::EMPTY;
Node *u, *v = Node::EMPTY, *LCA = Node::EMPTY;
access(y), splay(y);
for (u = x; u != Node::EMPTY; u = u->fa) {
splay(u);
if (u->fa == Node::EMPTY) {
LCA = u;
}
u->ch[1] = v;
v = u;
v->pushup();
}
return LCA;
}
int path(Node *x, Node *y) {
int ret;
Node *u, *v = Node::EMPTY;
access(y), splay(y);
for (u = x; u != Node::EMPTY; u = u->fa) {
splay(u), u->pushdown();
if (u->fa == Node::EMPTY) {
ret = u->ch[1]->size + v->size;
}
u->ch[1] = v;
v = u;
v->pushup();
}
return ret;
}
inline int label(Node *x) {
return x - _mem;
}
} tree;
LCT::Node *LCT::Node::EMPTY;
LCT::Node *A[100005], *node_x, *node_rt;
int main() {
int n, m, x, y, c, u, v;
char cmd[8];
while (scanf("%d %d", &n, &m) == 2) {
tree.init();
for (int i = 1; i <= n; i++)
A[i] = tree.newNode();
for (int i = 0; i < m; i++) {
scanf("%s", cmd);
if (cmd[0] == 'n') {
scanf("%d %d", &x, &y);
tree.cut(A[x]);
tree.link(A[x], A[y]);
} else if (cmd[0] == 's') {
scanf("%d %d", &x, &y);
node_x = tree.lca(A[x], A[y]);
int lca = tree.label(node_x);
if (lca == 0) {
puts("-1");
} else {
node_rt = tree.find(A[lca]);
int p1, p2;
p1 = tree.path(A[x], A[y]) + 1;
p2 = tree.path(A[lca], node_rt) + 1;
int a = p2*2, b = p1 + p2*2 - 1, g;
g = __gcd(a, b), a /= g, b /= g;
printf("%d/%d\n", a, b);
}
}
}
}
return 0;
}