// ~~ icebear ~~
#include <bits/stdc++.h>
using namespace std;
#define int long long
typedef long long ll;
typedef pair<int, int> ii;
typedef pair<int, ii> iii;
 
template<class T>
    bool minimize(T &a, const T &b) {
        if (a > b) return a = b, true;
        return false;
    }
 
template<class T>
    bool maximize(T &a, const T &b) {
        if (a < b) return a = b, true;
        return false;
    }
 
#define FOR(i,a,b) for(int i=(a); i<=(b); ++i)
#define FORR(i,a,b) for(int i=(a); i>=(b); --i)
#define REP(i, n) for(int i=0; i<(n); ++i)
#define RED(i, n) for(int i=(n)-1; i>=0; --i)
#define MASK(i) (1LL << (i))
#define BIT(S, i) (((S) >> (i)) & 1)
#define mp make_pair
#define pb push_back
#define fi first
#define se second
#define all(x) x.begin(), x.end()
#define task "icebear"
/*END OF TEMPLATE. ICEBEAR AND THE CAT WILL WIN VOI26 */
 
const int MOD = 1e9 + 7;
const int inf = 1e9 + 27092008;
const ll INF = 1e18 + 27092008;
const int N = 2e5 + 5;
const int inv6 = 166666668;
int numQuery, total;
int L[2709], H[2709];
 
int C3(int n) {
    return 1LL * n % MOD * (n - 1) % MOD * (n - 2) % MOD * inv6 % MOD;
}
 
int solve(int mask, int sum) {
    REP(i, 4) if (BIT(mask, i)) sum -= H[i] + 1;
    if (sum < 0) return 0;
    return C3(sum + 3);
}
 
void init(void) {
    cin >> numQuery;
}
 
void process(void) {
    while(numQuery--) {
        REP(i, 4) cin >> L[i] >> H[i];
        cin >> total;
        REP(i, 4) {
            total -= L[i];
            H[i] -= L[i];
        }
 
        int ans = 0;
        REP(mask, MASK(4)) ans = (ans + solve(mask, total) * (__builtin_popcount(mask) & 1 ? MOD - 1 : +1) % MOD) % MOD;
        cout << ans << '\n';
    }
}
 
signed main() {
    ios_base::sync_with_stdio(0);
    cin.tie(0); cout.tie(0);
    if (fopen(task".inp", "r")) {
        freopen(task".inp", "r", stdin);
        freopen(task".out", "w", stdout);
    }
    int tc = 1;
//    cin >> tc;
    while(tc--) {
        init();
        process();
    }
    return 0;
}
 
 
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