#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
const int N = 5e4 + 10;
ll a[N];
ll b[N];
unordered_map<int,int> q;
void solve()
{
    q.clear();
    ll n, k;
    cin >> n >> k;
    for (int i = 1; i <= n; i++) {
        cin >> a[i];
    }
    ll need = n - 1;
    for (int i = 1; i < n; i++) {
        ll x = a[i], y = a[i + 1];
        if (x > y) {
            swap(x, y);
        } else if (x == y) {
            need--;
        }
        ll add = y - x;
        for (int j = 1; j * j <= add; j++) {
            if ((add % j)) continue ;
            if (j > x && j + add == y + (j - x) && (j - x) <= k) {
                q[j - x]++;
            }
            ll now = add / j;
            if (now == j) continue ;
            if (now > x && now + add == y + (now - x) && (now - x) <= k) {
                q[now - x]++;
            }
        }
    }
    if (!need) {
        cout << k << ' ' << 1ll * k * (k + 1) / 2 << '\n';
        return ;
    }
    ll sum = 0, ans = 0;
    for (auto [x, y]: q) {
        if (y != need) continue ;
        for (int i = 1; i <= n; i++) {
            b[i] = a[i] + x;
        }
        bool use = 1;
        deque<int> s;
        for (int i = 1; i <= n; i++) {
            while (s.size() && s.back() > b[i]) {
                ll x = b[i], y = s.back();
                if ((x % y) && (y % x)) {
                    use = 0;
                    break;
                }
                s.pop_back();
            }
            if (s.size()) {
                ll x = b[i], y = s.back();
                if ((x % y) && (y % x)) {
                    use = 0;
                    break;
                }
            }
            s.push_back(b[i]);
        }
        if (use) {
            cout << x << '\n';
            sum = sum + x;
            ans++;
        }
    }
    cout << ans << ' ' << sum << '\n';
}
int main()
{
    ios::sync_with_stdio(false);
    cin.tie(nullptr);
    cout.tie(nullptr);
    int t=1;
    cin>>t;
    while(t--)
    solve();
    return 0;
}
/*
1 2
2 3


从小到大
20 10 2 10 20
*/