#include <bits/stdc++.h>
using namespace std;
typedef long long LL;
const int MOD = 998244353;
const int N = 205;


LL power(LL x, LL y) {
    LL ret = 1;
    for ( ; y; y >>= 1) {
        if (y & 1) ret = ret * x % MOD;
        x = x * x % MOD;
    }
    return ret;
}

int n, m, nn, K;
vector < pair <int, int> > E[N];
int tr[N][N], ans[N][N], tmp[N][N];


void mul(int a[N][N], int b[N][N]) {
    for (int i = 1; i <= nn; i++)
        for (int j = 1; j <= nn; j++)
            tmp[i][j] = 0;
    for (int i =1 ; i <= nn; i++)
        for (int j = 1; j <= nn; j++)
            for (int k = 1; k <= nn; k++) 
                tmp[i][k] = (tmp[i][k] + (LL)a[i][j] * b[j][k]) % MOD;
    for (int i = 1; i <= nn; i++)
        for (int j = 1; j <= nn; j++)
            a[i][j] = tmp[i][j];
}

void work() {
    scanf("%d%d%d", &n, &m, &K);
    nn = 2 * n;
    for (int i = 1; i <= n; i++) E[i].clear();
    for (int i = 1; i <= m; i++) {
        int u, v, w;
        scanf("%d%d%d", &u, &v, &w);
        E[u].push_back({v, w});
        E[v].push_back({u, w});
    }
    for (int i = 1; i <= nn; i++)
        for (int j = 1; j <= nn; j++)
            tr[i][j] = 0;
    for (int i = 1; i <= n; i++) {
        int no = (i << 1) - 1, yes = i << 1;
        int deg = E[i].size();
        if (!deg) continue;
        int inv = power(deg, MOD - 2);
        for (auto v : E[i]) {
            int j = (v.first << 1) - 1, k = v.second;
            tr[no][j + k] = inv;
            tr[yes][j + (k ^ 1)] = inv;
        }
    }

    for (int i = 1; i <= nn; i++)
        for (int j = 1; j <= nn; j++)
            ans[i][j] = 0;
    ans[1][1] = 1;
    for ( ; K; K >>= 1) {
        if (K & 1) mul(ans, tr);
        mul(tr, tr);
    }

    int tot = 0;
    for (int i = 1; i <= nn; i++) {
        tot += ans[1][i];    
        tot %= MOD;
    }
    printf("%d\n", int (ans[1][nn] * power(tot, MOD - 2) % MOD));
}

int main() {
    int T;
    scanf("%d", &T);
    while (T--) work();
}