#include <bits/stdc++.h>
using namespace std;

typedef long long ll;
typedef pair<int, int> pi;
typedef pair<ll,ll> pl;
typedef vector<int> vi;
typedef vector<ll> vl;

#define FOR(i, a, b) for (int i=a; i<(b); i++)
#define F0R(i, a) for (int i=0; i<(a); i++)
#define FORd(i,a,b) for (int i = (b)-1; i >= a; i--)
#define F0Rd(i,a) for (int i = (a)-1; i >= 0; i--)
#define trav(a,x) for (auto& a : x)

#define sz(x) (int)(x).size()
#define pb push_back
#define f first
#define s second
#define lb lower_bound
#define ub upper_bound
#define all(x) x.begin(), x.end()
#define ins insert

void solve() {
    int N, M; cin >> N >> M;
    vector<int> graph[2*N];
    F0R(i, M) {
        int X, Y; cin >> X >> Y; X--; Y--;
        graph[X].pb(Y+N);
        graph[X+N].pb(Y);
        graph[Y].pb(X+N);
        graph[Y+N].pb(X);
    }
    int dist[2*N]; F0R(i, 2*N) dist[i] = 1000000;
    queue<int> q;
    q.push(0);
    dist[0] = 0;
    while (!q.empty()) {
        int x = q.front(); q.pop();
        trav(a, graph[x]) {
            if (dist[a] > dist[x] + 1) {
                dist[a] = dist[x] + 1; q.push(a);
            }
        }
    }
    if (dist[N] > 2*N+10) {
        cout << N-1 << endl; return;
    }
    int ans = 0;
    map<int, int> cnt[4*N+10];
    F0R(i, N) {
        int x = min(dist[i], dist[i+N]); int y = max(dist[i], dist[i+N]);
        cnt[x+y][x]++;
    }

    F0Rd(m, 4*N+10) {
        int lst = -100;
        int cur = 0;
        trav(a, cnt[m]) {
            if (a.s == 0) continue;
            //cout << m << " " << a.f << " " << a.s << endl;
            if (lst < a.f-1) {
                if (lst * 2 + 1 == m) {
                    ans += (cur+1)/2;
                } else ans += cur;
                cur = 0;
            }
            lst = a.f;
            if (m >= 2 && cnt[m-2][a.f-1]) {
                ans += max(cur, a.s);
                cur = min(cur, a.s);
            } else {
                ans += max(cur, a.s);
                cur = a.s;
            }
        }
        if (lst*2+1 == m) {
            ans += (cur+1)/2;
        } else ans += cur;

    }
    ans--;
    /*sort(all(ps));
    trav(a, ps) {
        cout << a.f << " " << a.s << endl;
    }
    FOR(i, 1, 2*N+10) {
        for (auto it = cnt[i].rbegin(); it != cnt[i].rend(); it++) {
            int k = it->s;
            int p = it->f;
            k -= min(k, cnt[i-1][p]);
            int x = min(k, cnt[i-1][p-2]);
            cnt[i-1][p-2] -= x;
            k -= x;
            ans += k; if (p == 1) ans -= k/2;
        }
    }
    int on[2*N+10], off[2*N+10]; F0R(i, 2*N+10) on[i] = 0, off[i] = 0;
    int flow[2*N+10]; F0R(i, 2*N+10) flow[i] = 0;
    F0R(i, N) {
        int x = min(dist[i], dist[i+N]); int y = max(dist[i], dist[i+N]);
        on[x]++; if (y < 2*N+10) off[y]++;
        if (y == x+1) {
            off[y]--; flow[y]++;
            cout << i << " flows" << endl;
        }
        cout << y << " "<< y-x << endl;

    }

    bool found = false;
    FOR(i, 1, 2*N+10) {
        if (!found) {
            ans += on[i] + max(off[i] - off[i-1] - flow[i-1], 0) + (flow[i]+1)/2;
            found = true;
        } else {
            int num = off[i-1] + flow[i-1];
            int x = min(num, off[i]);
            int k = off[i] - x;
            num -= x;
            int l = flow[i] - min(num, flow[i]);
            ans += on[i] + k + (l+1)/2;
        }
        //cout << i << ": " << on[i] << " " << off[i] << " " << flow[i] << " " << ans << endl;
    }*/

    cout << ans << endl;
}

int main() {
	ios_base::sync_with_stdio(0); cin.tie(0);

    int T; cin >> T;
    while(T--) {
        solve();
    }

	return 0;
}