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

#define fast_io ios::sync_with_stdio(0); cin.tie(0); cout.tie(0)

#define int long long
#define pb push_back
#define ff first
#define ss second
#define all(x) (x).begin(), (x).end()
#define rall(x) (x).rbegin(), (x).rend()
#define sz(x) ((int)(x).size())
#define endl '\n'
#define yes cout << "yes\n"
#define no cout << "no\n"

#define rep(i,a,b) for(int i=a;i<b;++i)
#define per(i,a,b) for(int i=b-1;i>=a;--i)
#define each(x, a) for (auto& x : a)

const int INF = 1e18;
const int MOD = 998244353;
const int N = 2e5 + 5;

int gcd(int a, int b) { return b == 0 ? a : gcd(b, a % b); }
int lcm(int a, int b) { return (a / gcd(a, b)) * b; }
int power(int a, int b, int m = MOD) {
    int res = 1;
    while (b > 0) {
        if (b & 1) res = res * a % m;
        a = a * a % m;
        b >>= 1;
    }
    return res;
}
int modinv(int a, int m = MOD) {
    return power(a, m - 2, m);
}

void solve() {
    int n;
    cin >> n;
    vector<int> a(n + 1);
    int sum = 0;
    rep(i, 0, n + 1) {
        cin >> a[i];
        sum += a[i];
    }

    int k = sum / n;
    int r = sum % n;

    int heavy_cnt = 0;
    rep(i, 1, n + 1) {
        if (a[i] > k + 1) {
            cout << 0 << endl;
            return;
        }
        if (a[i] == k + 1) {
            heavy_cnt++;
        }
    }

    if (heavy_cnt > r) {
        cout << 0 << endl;
        return;
    }

    int ans = 1;
    rep(i, 0, heavy_cnt) {
        ans = (ans * (r - i)) % MOD;
    }

    rep(i, 1, n - heavy_cnt + 1) {
        ans = (ans * i) % MOD;
    }

    cout << ans << endl;
}

int32_t main() {
    fast_io;
    int t;
    cin >> t;
    while (t--) {
        solve();
    }
    return 0;
}