// Skyqwq
#include <bits/stdc++.h>

#define pb push_back
#define fi first
#define se second
#define mp make_pair

using namespace std;

typedef pair<int, int> PII;
typedef long long LL;

template <typename T> bool chkMax(T &x, T y) { return (y > x) ? x = y, 1 : 0; }
template <typename T> bool chkMin(T &x, T y) { return (y < x) ? x = y, 1 : 0; }

template <typename T> void inline read(T &x) {
    int f = 1; x = 0; char s = getchar();
    while (s < '0' || s > '9') { if (s == '-') f = -1; s = getchar(); }
    while (s <= '9' && s >= '0') x = x * 10 + (s ^ 48), s = getchar();
    x *= f;
}

const int N = 5e6 + 5, P = 998244353, M = P - 1;

int fact[N], infact[N], pa[N], ia[N];

int inline power(int a, int b) {
    int res = 1;
    while (b) {
        if (b & 1) res = (LL)res * a % P;
        a = (LL)a * a % P;
        b >>= 1;
    }
    return res;
}

void inline add(int &x, int y) {
    x += y;
    if (x >= P) x -= P;
}

void inline factPrework(int n) {
    fact[0] = infact[0] = 1;
    for (int i = 1; i <= n; i++) fact[i] = (LL)fact[i - 1] * i % P;
    infact[n] = power(fact[n], P - 2);
    for (int i = n - 1; i; i--) infact[i] = infact[i + 1] * (i + 1ll) % P;
}

int inline C(int a, int b) {
    if (a < b || a < 0 || b < 0) return 0;
    return (LL)fact[a] * infact[b] % P * infact[a - b] % P;
}

int n, m, l, inv2 = (P + 1) / 2;
LL num;

int inline get(int k) {
    int v = 1ll * C(n, k) * C(m, k) % P * C(l, k) % P * fact[k] % P * fact[k] % P * fact[k] % P;
    v = 1ll * v * ia[k] % P;
    return v;
}

int inline g(int i) {
    return (1ll * n * m % P * l % P - 1ll * (n - i) * (m - i) % P * (l - i) % P + P) % P;
}

int main() {
    factPrework(5e6);
    int T; read(T);
    while (T--) {
        int k; read(n), read(m), read(l), read(k);
        int len = min(n, min(m, l));
        pa[0] = ia[0] = 1;
        for (int i = 1; i <= len; i++)
            pa[i] = 1ll * pa[i - 1] * g(i) % P;
        ia[len] = power(pa[len], P - 2);
        for (int i = len - 1; i; i--)
            ia[i] = 1ll * ia[i + 1] * g(i + 1) % P;
        int ans = 0;
        for (int i = k; i <= len; i++) {
            int w = 1ll * get(i) * C(i, k) % P;
            if ((i - k) & 1) add(ans, P - w);
            else add(ans, w);
        }
        printf("%d\n", ans);
    }    
    return 0;
}