#include <cassert>
#include <cmath>
#include <cstdint>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <algorithm>
#include <bitset>
#include <complex>
#include <deque>
#include <functional>
#include <iostream>
#include <limits>
#include <map>
#include <numeric>
#include <queue>
#include <set>
#include <sstream>
#include <string>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>

using namespace std;

using Int = long long;

template <class T1, class T2> ostream &operator<<(ostream &os, const pair<T1, T2> &a) { return os << "(" << a.first << ", " << a.second << ")"; };
template <class T> ostream &operator<<(ostream &os, const vector<T> &as) { const int sz = as.size(); os << "["; for (int i = 0; i < sz; ++i) { if (i >= 256) { os << ", ..."; break; } if (i > 0) { os << ", "; } os << as[i]; } return os << "]"; }
template <class T> void pv(T a, T b) { for (T i = a; i != b; ++i) cerr << *i << " "; cerr << endl; }
template <class T> bool chmin(T &t, const T &f) { if (t > f) { t = f; return true; } return false; }
template <class T> bool chmax(T &t, const T &f) { if (t < f) { t = f; return true; } return false; }
#define COLOR(s) ("\x1b[" s "m")


template <class T> void bAdd(vector<T> &bit, int pos, const T &val) {
  const int bitN = bit.size();
  for (int x = pos; x < bitN; x |= x + 1) bit[x] += val;
}
template <class T> T bSum(const vector<T> &bit, int pos) {
  T ret = 0;
  for (int x = pos; x > 0; x &= x - 1) ret += bit[x - 1];
  return ret;
}
template <class T> T bSum(const vector<T> &bit, int pos0, int pos1) {
  return bSum(bit, pos1) - bSum(bit, pos0);
}


struct Hld {
  int n, rt;
  // needs to be tree
  // vertex lists
  // modified in build(rt) (parent removed, heavy child first)
  vector<vector<int>> graph;
  vector<int> sz, par, dep;
  int zeit;
  vector<int> dis, fin, sid;
  // head vertex (minimum depth) in heavy path
  vector<int> head;

  Hld() : n(0), rt(-1), zeit(0) {}
  explicit Hld(int n_) : n(n_), rt(-1), graph(n), zeit(0) {}
  void ae(int u, int v) {
    assert(0 <= u); assert(u < n);
    assert(0 <= v); assert(v < n);
    graph[u].push_back(v);
    graph[v].push_back(u);
  }

  void dfsSz(int u) {
    sz[u] = 1;
    for (const int v : graph[u]) {
      auto it = std::find(graph[v].begin(), graph[v].end(), u);
      if (it != graph[v].end()) graph[v].erase(it);
      par[v] = u;
      dep[v] = dep[u] + 1;
      dfsSz(v);
      sz[u] += sz[v];
    }
  }
  void dfsHld(int u) {
    dis[u] = zeit++;
    const int deg = graph[u].size();
    if (deg > 0) {
      int vm = graph[u][0];
      int jm = 0;
      for (int j = 1; j < deg; ++j) {
        const int v = graph[u][j];
        if (sz[vm] < sz[v]) {
          vm = v;
          jm = j;
        }
      }
      swap(graph[u][0], graph[u][jm]);
      head[vm] = head[u];
      dfsHld(vm);
      for (int j = 1; j < deg; ++j) {
        const int v = graph[u][j];
        head[v] = v;
        dfsHld(v);
      }
    }
    fin[u] = zeit;
  }
  void build(int rt_) {
    assert(0 <= rt_); assert(rt_ < n);
    rt = rt_;
    sz.assign(n, 0);
    par.assign(n, -1);
    dep.assign(n, -1);
    dep[rt] = 0;
    dfsSz(rt);
    zeit = 0;
    dis.assign(n, -1);
    fin.assign(n, -1);
    head.assign(n, -1);
    head[rt] = rt;
    dfsHld(rt);
    assert(zeit == n);
    sid.assign(n, -1);
    for (int u = 0; u < n; ++u) sid[dis[u]] = u;
  }

  friend ostream &operator<<(ostream &os, const Hld &hld) {
    const int maxDep = *max_element(hld.dep.begin(), hld.dep.end());
    vector<string> ss(2 * maxDep + 1);
    int pos = 0, maxPos = 0;
    for (int j = 0; j < hld.n; ++j) {
      const int u = hld.sid[j];
      const int d = hld.dep[u];
      if (hld.head[u] == u) {
        if (j != 0) {
          pos = maxPos + 1;
          ss[2 * d - 1].resize(pos, '-');
          ss[2 * d - 1] += '+';
        }
      } else {
        ss[2 * d - 1].resize(pos, ' ');
        ss[2 * d - 1] += '|';
      }
      ss[2 * d].resize(pos, ' ');
      ss[2 * d] += std::to_string(u);
      if (maxPos < static_cast<int>(ss[2 * d].size())) {
        maxPos = ss[2 * d].size();
      }
    }
    for (int d = 0; d <= 2 * maxDep; ++d) os << ss[d] << '\n';
    return os;
  }

  bool contains(int u, int v) const {
    return (dis[u] <= dis[v] && dis[v] < fin[u]);
  }
  int lca(int u, int v) const {
    assert(0 <= u); assert(u < n);
    assert(0 <= v); assert(v < n);
    for (; head[u] != head[v]; ) (dis[u] > dis[v]) ? (u = par[head[u]]) : (v = par[head[v]]);
    return (dis[u] > dis[v]) ? v : u;
  }
  int jumpUp(int u, int d) const {
    assert(0 <= u); assert(u < n);
    assert(d >= 0);
    if (dep[u] < d) return -1;
    const int tar = dep[u] - d;
    for (u = head[u]; ; u = head[par[u]]) {
      if (dep[u] <= tar) return sid[dis[u] + (tar - dep[u])];
    }
  }
  int jump(int u, int v, int d) const {
    assert(0 <= u); assert(u < n);
    assert(0 <= v); assert(v < n);
    assert(d >= 0);
    const int l = lca(u, v);
    const int du = dep[u] - dep[l], dv = dep[v] - dep[l];
    if (d <= du) {
      return jumpUp(u, d);
    } else if (d <= du + dv) {
      return jumpUp(v, du + dv - d);
    } else {
      return -1;
    }
  }
  // [u, v) or [u, v]
  template <class F> void doPathUp(int u, int v, bool inclusive, F f) const {
    assert(contains(v, u));
    for (; head[u] != head[v]; u = par[head[u]]) f(dis[head[u]], dis[u] + 1);
    if (inclusive) {
      f(dis[v], dis[u] + 1);
    } else {
      if (v != u) f(dis[v] + 1, dis[u] + 1);
    }
  }
  // not path order, include lca(u, v) or not
  template <class F> void doPath(int u, int v, bool inclusive, F f) const {
    const int l = lca(u, v);
    doPathUp(u, l, false, f);
    doPathUp(v, l, inclusive, f);
  }

  // (vs, ps): compressed tree
  // vs: DFS order (sorted by dis)
  // vs[ps[x]]: the parent of vs[x]
  // ids[vs[x]] = x, not set for non-tree vertex
  vector<int> ids;
  pair<vector<int>, vector<int>> compress(vector<int> us) {
    // O(n) first time
    ids.resize(n, -1);
    std::sort(us.begin(), us.end(), [&](int u, int v) -> bool {
      return (dis[u] < dis[v]);
    });
    us.erase(std::unique(us.begin(), us.end()), us.end());
    int usLen = us.size();
    assert(usLen >= 1);
    for (int x = 1; x < usLen; ++x) us.push_back(lca(us[x - 1], us[x]));
    std::sort(us.begin(), us.end(), [&](int u, int v) -> bool {
      return (dis[u] < dis[v]);
    });
    us.erase(std::unique(us.begin(), us.end()), us.end());
    usLen = us.size();
    for (int x = 0; x < usLen; ++x) ids[us[x]] = x;
    vector<int> ps(usLen, -1);
    for (int x = 1; x < usLen; ++x) ps[x] = ids[lca(us[x - 1], us[x])];
    return make_pair(us, ps);
  }
};

////////////////////////////////////////////////////////////////////////////////

// iterator find_by_order(k): 0-indexed
// size_type order_of_key(key): min id s.t. >= key
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
template <class T> using rbtree = __gnu_pbds::tree<
  T,
  __gnu_pbds::null_type,
  std::less<T>,
  __gnu_pbds::rb_tree_tag,
  __gnu_pbds::tree_order_statistics_node_update
>;


int N, M;
vector<int> A, B;

vector<vector<int>> G;


namespace brute {
// 0: first, nigeru; 1: second, ou
int win[2][2010][2010];
int deg[2][2010][2010];
Int run() {
  vector<int> degTree(N, 0);
  for (int i = 0; i < N - 1; ++i) {
    ++degTree[A[i]];
    ++degTree[B[i]];
  }
  memset(win, ~0, sizeof(win));
  memset(deg, 0, sizeof(deg));
  queue<pair<int, pair<int, int>>> que;
  for (int u = 0; u < N; ++u) for (int v = 0; v < N; ++v) {
    if (u == v) {
      for (int t = 0; t < 2; ++t) {
        win[t][u][v] = t;
        que.emplace(t, make_pair(u, v));
      }
    } else {
      deg[0][u][v] = 1 + (int)G[u].size();
      deg[1][u][v] = 1 + degTree[v];
    }
  }
  for (; !que.empty(); ) {
    const int t = que.front().first;
    const int u = que.front().second.first;
    const int v = que.front().second.second;
    que.pop();
    auto reach = [&](int tt, int uu, int vv) -> void {
      if (!~win[tt][uu][vv]) {
        if (win[t][u][v]) {
          if (!--deg[tt][uu][vv]) {
            win[tt][uu][vv] = 0;
            que.emplace(tt, make_pair(uu, vv));
          }
        } else {
          win[tt][uu][vv] = 1;
          que.emplace(tt, make_pair(uu, vv));
        }
      }
    };
    if (t) {
      // reverse nigeru
      reach(0, u, v);
      for (const int i : G[u]) {
        reach(0, A[i] ^ B[i] ^ u, v);
      }
    } else {
      // reverse ou
      reach(1, u, v);
      for (const int i : G[v]) if (i < N - 1) {
        reach(1, u, A[i] ^ B[i] ^ v);
      }
    }
  }
for(int t=0;t<2;++t)for(int u=0;u<N;++u){cerr<<"win["<<t<<"]["<<u<<"] = ";pv(win[t][u],win[t][u]+N);}
  Int ans = 0;
  for (int u = 0; u < N; ++u) for (int v = 0; v < N; ++v) if (u != v) {
    if (win[0][u][v]) {
      ++ans;
    }
  }
  return ans;
}
}  // brute


namespace one {
vector<int> par;
void dfs(int u, int p) {
  par[u] = p;
  for (const int i : G[u]) if (i < N - 1) {
    const int v = A[i] ^ B[i] ^ u;
    if (p != v) {
      dfs(v, u);
    }
  }
}
vector<int> on;
vector<vector<int>> dss;
void DFS(int k, int u, int p, int d) {
  dss[k].push_back(d);
  for (const int i : G[u]) if (i < N - 1) {
    const int v = A[i] ^ B[i] ^ u;
    if (p != v && !on[v]) {
      DFS(k, v, u, d + 1);
    }
  }
}
Int run() {
  const int s = A[N - 1];
  const int t = B[N - 1];
  par.assign(N, -1);
  dfs(s, -1);
  vector<int> path;
  for (int u = t; ~u; u = par[u]) {
    path.push_back(u);
  }
  reverse(path.begin(), path.end());
  const int len = (int)path.size() - 1;
// cerr<<"path = "<<path<<endl;
  Int ans = 0;
  if (len >= 3) {
    on.assign(N, 0);
    for (int k = 0; k <= len; ++k) {
      on[path[k]] = 1;
    }
    dss.assign(len + 1, {});
    for (int k = 0; k <= len; ++k) {
      DFS(k, path[k], -1, 0);
    }
    // go to s
    {
      vector<int> bit(N, 0);
      for (int k = 0; k <= len; ++k) {
        for (const int d : dss[k]) bAdd(bit, k + d, +1);
        for (const int d : dss[k]) ans += bSum(bit, k + d);
      }
    }
    // go to t
    {
      vector<int> bit(N, 0);
      for (int k = len; k >= 0; --k) {
        for (const int d : dss[k]) ans += bSum(bit, (len - k) + d);
        for (const int d : dss[k]) bAdd(bit, (len - k) + d, +1);
      }
    }
  }
  return ans;
}
}  // one


namespace fast {
Int ans;
Hld hld;
vector<vector<int>> skip;
vector<vector<pair<int, int>>> badSkip;
vector<int> on;

vector<vector<int>> graph;
vector<int> sz, del;
void dfsSz(int u, int p) {
  sz[u] = 1;
  for (const int v : graph[u]) if (p != v) {
    dfsSz(v, u);
    sz[u] += sz[v];
  }
}
string dfsString(int u, int p) {
  ostringstream oss;
  oss << "[" << u;
  for (const int v : graph[u]) if (!del[v] && p != v) {
    oss << " " << dfsString(v, u);
  }
  oss << "]";
  return oss.str();
}
vector<int> costs;
vector<vector<int>> css[2];
Int solveBad(int jj, int u, int p) {
  auto res = equal_range(css[1][jj].begin(), css[1][jj].end(), (costs[u] - 0) + 1);
  Int ret = res.second - res.first;
  for (const int i : G[u]) if (i < N - 1) {
    const int v = A[i] ^ B[i] ^ u;
    if (!on[v] && p != v) {
      ret += solveBad(jj, v, u);
    }
  }
  return ret;
}
void sub(int j, int u, int p, int p2, int d, int e) {
  for (const int v : skip[u]) {
    if (p2 == v) {
      costs[u] = costs[p2] + 1;
    } else if (on[v] == 1) {
      costs[u] = 0;
    }
  }
  css[0][j].push_back(costs[u] - d);
  css[1][j].push_back(e + d);
  for (const int i : G[u]) if (i < N - 1) {
    const int v = A[i] ^ B[i] ^ u;
    if (!on[v] && p != v) {
      costs[v] = costs[u] + 1;
      sub(j, v, u, p, d, e + 1);
    }
  }
}
void dfs(int j, int u, int p, int d) {
  costs[u] = 0;
  on[p] = 2;
  sub(j, u, -1, -1, d, 0);
  on[p] = 1;
  for (const int v : graph[u]) if (!del[v] && p != v) {
    dfs(j, v, u, d + 1);
  }
}
void solveSubtree(int depth, int r) {
#ifdef LOCAL
  cerr << string(2 * depth, ' ') << "solveSubtree " << dfsString(r, -1) << endl;
#endif
  vector<int> vs;
  for (const int v : graph[r]) if (!del[v]) {
    vs.push_back(v);
  }
  sort(vs.begin(), vs.end());
  const int len = vs.size();
  for (int h = 0; h < 2; ++h) {
    css[h].assign(len + 2, {});
  }
  for (int j = 0; j < len; ++j) {
    dfs(j, vs[j], r, 1);
  }
  costs[r] = 0;
  sub(len, r, -1, -1, 0, 0);
  for (int h = 0; h < 2; ++h) {
    for (int j = 0; j <= len; ++j) {
      css[h][len + 1].insert(css[h][len + 1].end(), css[h][j].begin(), css[h][j].end());
    }
    for (int j = 0; j <= len + 1; ++j) {
      sort(css[h][j].begin(), css[h][j].end());
    }
  }
  Int sum = 0;
  for (int j = 0; j <= len + 1; ++j) {
    int pos0 = 0;
    for (int pos1 = 0; pos1 < (int)css[1][j].size(); ++pos1) {
      for (; pos0 < (int)css[0][j].size() && css[0][j][pos0] < css[1][j][pos1]; ++pos0) {}
      sum += ((j <= len) ? -1 : +1) * pos0;
    }
  }
  
  Int bad = 0;
  map<int, vector<int>> jjss;
  for (const auto &e : badSkip[r]) {
    for (const int u : {e.first, e.second}) if (!on[u]) {
      const int v = e.first ^ e.second ^ u;
      auto jj = lower_bound(vs.begin(), vs.end(), v) - vs.begin();
      if (jj < len && vs[jj] == v) {
// cerr<<COLOR("91")<<string(2*depth,' ')<<"bad e = "<<e<<", u = "<<u<<", jj = "<<jj<<COLOR()<<endl;
        jjss[u].push_back(jj);
      }
    }
  }
  for (auto &kv : jjss) {
    const int u = kv.first;
    auto jjs = kv.second;
    sort(jjs.begin(), jjs.end());
    if (jjs[0] == jjs.back()) {
      bad += solveBad(jjs[0], u, r);
    }
  }
  
#ifdef LOCAL
cerr<<string(2*depth,' ')<<"vs = "<<vs<<", costs = "<<costs<<", css = ";pv(css,css+2);
cerr<<string(2*depth,' ')<<"sum = "<<sum<<", bad = "<<bad<<endl;
#endif
  ans += (sum - bad);
}
void solveRec(int depth, int u) {
  for (; ; ) {
    int vm = -1;
    for (const int v : graph[u]) if (!del[v]) {
      if (!~vm || sz[vm] < sz[v]) {
        vm = v;
      }
    }
    if (!~vm || 2 * sz[vm] <= sz[u]) {
      solveSubtree(depth, u);
      del[u] = 1;
      for (const int v : graph[u]) if (!del[v]) {
        solveRec(depth + 1, v);
      }
      break;
    } else {
      sz[u] -= sz[vm];
      sz[vm] += sz[u];
      u = vm;
    }
  }
}
void centroidDecomp(int r) {
  sz.assign(N, 0);
  dfsSz(r, -1);
  del.assign(N, 0);
  costs.assign(N, 0);
  solveRec(0, r);
}

pair<rbtree<pair<int, int>> *, rbtree<pair<int, int>> *> solveSame(int u, int p, int p2, int e) {
  for (const int v : skip[u]) {
    if (p2 == v) {
      costs[u] = costs[p2] + 1;
    } else if (on[v] == 1) {
      costs[u] = 0;
    }
  }
  pair<rbtree<pair<int, int>> *, rbtree<pair<int, int>> *> ret;
  ret.first = new rbtree<pair<int, int>>;
  ret.second = new rbtree<pair<int, int>>;
  ret.first->insert(make_pair(costs[u], u));
  ret.second->insert(make_pair(e, u));
  for (const int i : G[u]) if (i < N - 1) {
    const int v = A[i] ^ B[i] ^ u;
    if (!on[v] && p != v) {
      auto res = solveSame(v, u, p, e + 1);
      if (ret.first->size() < res.first->size()) {
        swap(ret, res);
      }
      // c' < e' - e + costs[u]  (?)
      Int sum = 0;
      for (const auto &kv : *res.second) {
        const int ee = kv.first;
        sum += (int)ret.first->order_of_key(make_pair(ee - e + costs[u], -1));
      }
      for (const auto &kv : *res.first) {
        const int cc = kv.first;
        sum += ((int)ret.second->size() - (int)ret.second->order_of_key(make_pair(cc - costs[u] + e + 1, -1)));
      }
      ans += sum;
      for (const auto &kv : *res.first) {
        ret.first->insert(kv);
      }
      for (const auto &kv : *res.second) {
        ret.second->insert(kv);
      }
    }
  }
  return ret;
}

Int run() {
  ans = 0;
  hld = Hld(N);
  for (int i = 0; i < N - 1; ++i) {
    hld.ae(A[i], B[i]);
  }
  hld.build(0);
#ifdef LOCAL
cerr<<hld<<endl;
#endif
  vector<int> tar(N, 0);
  skip.assign(N, {});
  badSkip.assign(N, {});
  for (int i = N - 1; i < M; ++i) {
    const int l = hld.lca(A[i], B[i]);
    const int d = hld.dep[A[i]] + hld.dep[B[i]] - 2 * hld.dep[l];
    if (d >= 3) {
      tar[A[i]] = tar[B[i]] = 1;
    } else if (d == 2) {
      skip[A[i]].push_back(B[i]);
      skip[B[i]].push_back(A[i]);
      if (l != A[i] && l != B[i]) {
        badSkip[l].emplace_back(A[i], B[i]);
      }
    }
  }
  on.assign(N, 0);
  for (int j = N; --j >= 1; ) {
    const int u = hld.sid[j];
    tar[hld.par[u]] += tar[u];
  }
  for (int j = N; --j >= 1; ) {
    const int u = hld.sid[j];
    if (0 < tar[u] && tar[u] < tar[0]) {
      on[hld.par[u]] = on[u] = 1;
    }
  }
// cerr<<"on = "<<on<<endl;
  int r = -1;
  for (int u = 0; u < N; ++u) if (on[u]) {
    r = u;
    break;
  }
  if (~r) {
    graph.assign(N, {});
    for (int i = 0; i < N - 1; ++i) if (on[A[i]] && on[B[i]]) {
      graph[A[i]].push_back(B[i]);
      graph[B[i]].push_back(A[i]);
    }
    centroidDecomp(r);
    for (int u = 0; u < N; ++u) if (on[u]) {
      costs[u] = 0;
      solveSame(u, -1, -1, 0);
    }
  }
  return ans;
}
}  // fast


int main() {
  for (; ~scanf("%d%d", &N, &M); ) {
    M += (N - 1);
    A.resize(M);
    B.resize(M);
    for (int i = 0; i < M; ++i) {
      scanf("%d%d", &A[i], &B[i]);
      --A[i];
      --B[i];
    }
    
    G.assign(N, {});
    for (int i = 0; i < M; ++i) {
      G[A[i]].push_back(i);
      G[B[i]].push_back(i);
    }
    
    const Int ans = fast::run();
    printf("%lld\n", ans);
#ifdef LOCAL
const Int brt=brute::run();
if(brt!=ans){
 cerr<<"N = "<<N<<", M-(N-1) = "<<M-(N-1)<<endl;
 cerr<<"A = "<<A<<endl;
 cerr<<"B = "<<B<<endl;
 cerr<<"brt = "<<brt<<", ans = "<<ans<<endl;
}
assert(brt==ans);
#endif
  }
  return 0;
}