[BZOJ3772]精神污染

#include <iostream>
#include <cstdio>
#include <algorithm>
#include <cmath>
#include <stack>
#include <vector>
#include <queue>
#include <cstring>
#include <string>
#include <map>
#include <set>
using namespace std;

const int BufferSize = 1 << 16;
char buffer[BufferSize], *Head, *Tail;
inline char Getchar() {
	if(Head == Tail) {
		int l = fread(buffer, 1, BufferSize, stdin);
		Tail = (Head = buffer) + l;
	}
	return *Head++;
}
int read() {
	int x = 0, f = 1; char c = Getchar();
	while(!isdigit(c)){ if(c == ‘-‘) f = -1; c = Getchar(); }
	while(isdigit(c)){ x = x * 10 + c - ‘0‘; c = Getchar(); }
	return x * f;
}

#define maxn 100010
#define maxm 200010
#define maxnode 4000010
#define maxlog 17
#define LL long long

int ToT, sumv[maxnode], lc[maxnode], rc[maxnode];
void update(int& y, int x, int l, int r, int p, int v) {
	sumv[y = ++ToT] = sumv[x] + v;
	if(l == r) return ;
	int mid = l + r >> 1; lc[y] = lc[x]; rc[y] = rc[x];
	if(p <= mid) update(lc[y], lc[x], l, mid, p, v);
	else update(rc[y], rc[x], mid + 1, r, p, v);
	return ;
}
int query(int o, int l, int r, int ql, int qr) {
	if(!o) return 0;
	if(ql <= l && r <= qr) return sumv[o];
	int mid = l + r >> 1, ans = 0;
	if(ql <= mid) ans += query(lc[o], l, mid, ql, qr);
	if(qr > mid) ans += query(rc[o], mid + 1, r, ql, qr);
	return ans;
}

int n, m, head[maxn], next[maxm], to[maxm];
void AddEdge(int a, int b) {
	to[++m] = b; next[m] = head[a]; head[a] = m;
	swap(a, b);
	to[++m] = b; next[m] = head[a]; head[a] = m;
	return ;
}
struct Path {
	int a, b;
	Path() {}
	Path(int _, int __): a(_), b(__) {}
} ps[maxn];
int pm, phead[maxn], pnxt[maxn], pto[maxn];
void AddPath(int a, int b) {
	ps[++pm] = Path(a, b);
	pto[pm] = b; pnxt[pm] = phead[a]; phead[a] = pm;
	return ;
}

int fa[maxlog][maxn], dep[maxn], rt[maxn], dl[maxn], dr[maxn], clo;
void build(int u) {
	dl[u] = ++clo;
	for(int i = 1; i < maxlog; i++) fa[i][u] = fa[i-1][fa[i-1][u]];
	for(int e = head[u]; e; e = next[e]) if(to[e] != fa[0][u]) {
		dep[to[e]] = dep[u] + 1;
		fa[0][to[e]] = u;
		build(to[e]);
	}
	dr[u] = ++clo;
	return ;
}
int lca(int a, int b) {
	if(dep[a] < dep[b]) swap(a, b);
	for(int i = maxlog - 1; i >= 0; i--) if(dep[a] - dep[b] >= (1 << i)) a = fa[i][a];
	for(int i = maxlog - 1; i >= 0; i--) if(fa[i][a] != fa[i][b]) a = fa[i][a], b = fa[i][b];
	return a == b ? a : fa[0][b];
}
void build2(int u) {
	rt[u] = rt[fa[0][u]];
	for(int e = phead[u]; e; e = pnxt[e]) {
		update(rt[u], rt[u], 1, clo, dl[pto[e]], 1),
		update(rt[u], rt[u], 1, clo, dr[pto[e]], -1);
//		if(ToT % 10000 == 0) printf("ToT: %d\n", ToT);
	}
	for(int e = head[u]; e; e = next[e]) if(to[e] != fa[0][u]) build2(to[e]);
	return ;
}

LL gcd(LL a, LL b) { return b ? gcd(b, a % b) : a; }

int main() {
//	freopen("data.in", "r", stdin);
	n = read(); int tm = read();
	for(int i = 1; i < n; i++) {
		int a = read(), b = read();
		AddEdge(a, b);
	}
	while(tm--) {
		int a = read(), b = read();
		AddPath(a, b);
	}
	
	build(1); build2(1);
	LL ans = 0;
	for(int i = 1; i <= pm; i++) {
		int a = ps[i].a, b = ps[i].b, c = lca(a, b);
//		printf("lca(%d, %d) = %d\n", a, b, c);
		ans += (LL)query(rt[a], 1, clo, dl[c], dl[a]) - query(rt[fa[0][c]], 1, clo, dl[c], dl[a]);
		ans += (LL)query(rt[a], 1, clo, dl[c] + 1, dl[b]) - query(rt[fa[0][c]], 1, clo, dl[c] + 1, dl[b]);
		ans += (LL)query(rt[b], 1, clo, dl[c], dl[a]) - query(rt[c], 1, clo, dl[c], dl[a]);
		ans += (LL)query(rt[b], 1, clo, dl[c] + 1, dl[b]) - query(rt[c], 1, clo, dl[c] + 1, dl[b]);
		ans--;
	}
	
	LL bns = (LL)pm * (pm - 1) >> 1, g = gcd(ans, bns);
	ans /= g; bns /= g;
	printf("%lld/%lld\n", ans, bns);
	
	return 0;
}