// trace works only with c++ 14

#include<bits/stdc++.h>
using namespace std;
//#pragma comment (linker, "/STACK:256000000")
#define TRACE
#ifdef TRACE
#define trace(...) __f(#__VA_ARGS__, __VA_ARGS__)
template <typename Arg1>
void __f(const char* name, Arg1&& arg1) {
  cerr << name << " : " << arg1 << endl;
}

template <typename Arg1, typename... Args>
void __f(const char* names, Arg1&& arg1, Args&&... args) {
  const char* comma = strchr(names + 1, ',');
  cerr.write(names, comma - names) << " : " << arg1<<" | ";
  __f(comma+1, args...);
}
#else
#define trace(...)
#endif

#define all(a) a.begin(), a.end()
#define endl '\n'
#define mp make_pair
#define pb push_back
#define f first
#define s second
#define boost  ios_base::sync_with_stdio(false);
#define FOR(i, a, b) for (int i = (a); i < (b); ++i)
#define REP(i, n) FOR(i, 0, n)

typedef long long llint;
typedef long long ll ;
typedef pair<int, int> pii;
typedef vector<int> vi;
typedef vector<pii> vii;

const int mod = 1e9 + 7 ;
ll powmod(ll a,ll b) {ll res=1;if(a>=mod)a%=mod;for(;b;b>>=1){if(b&1)res=res*a;if(res>=mod)res%=mod;a=a*a;if(a>=mod)a%=mod;}return res;}
ll gcd(ll a , ll b){return a==0?b:gcd(b%a,a);}
/*---------------------------------------------------------------------------------------------------------------------*/
const int maxn = 800000 + 100;
const int inf = INT_MAX;
ll tree[maxn * 4];
ll w[maxn], d[maxn], z[maxn], s[maxn], g[maxn][3];
ll aw, bw, ad, bd, as, bs, s1, d1, w1;
ll n, m;
int MOD = 1000 * 1000 * 1000;
#define front 2
#define back 0
#define same 1
void build(int node, int a, int b)
{
    if(a == b)
    {
        tree[node] = 1;
        return;
    }
    build(node * 2, a, (a + b) / 2);
    build(node * 2 + 1, (a + b) / 2 + 1, b);
    tree[node] = 1;
}
ll query(int node, int a, int b, int i, int j)
{
    if(a > b || a > j || b < i || j < i)
        return 1;
    if(a >= i && b <= j)
        return tree[node];
    ll ret = query(node * 2, a, (a + b) / 2, i, j) * query(node * 2 + 1, (a + b) / 2 + 1, b, i, j);
    if(ret >= mod)
        ret %= mod;
    return ret;
}
ll upd(int node, int a, int b, int i)
{
    if(a > b)
        return 1;
    if( a > i || b < i)
        return tree[node];
    if(a == b)
    {
        tree[node] = g[a][1];
        //trace(tree[node], a, b, i);
        return tree[node];
    }
   ll ret1 = upd(node * 2, a, (a + b) / 2, i) * upd(node * 2 + 1, (a + b) / 2 + 1, b, i);
   if(ret1 >= mod)
        ret1 %= mod;
   ll ret2 = query(1, 1, n, a, (a + b) / 2 - 1) * query(1, 1, n, (a + b) / 2 + 2, b);
   if(ret2 >= mod)
        ret2 %= mod;
   ret2 = ret2 * g[(a + b) / 2][front];
   if(ret2 >= mod)
        ret2 %= mod;
   ret2 = ret2 * g[(a + b) / 2 + 1][back];
   if(ret2 >= mod)
        ret2 %= mod;
    //trace(ret1, ret2, a, b, i);
    ret1 += ret2;
   if(ret1 >= mod)
        ret1 -= mod;
    return tree[node] = ret1;
}
int main() {
    freopen("in.txt","r",stdin);
    freopen("out.txt","w",stdout);
    boost;cin.tie(0);
    int t, tt = 0, i;
    cin >> t;
    while(t--)
    {
        tt++;
        cout << "Case #" << tt << ": ";
        cin >> n >> m;
        cin >> w1 >> aw >> bw;
        cin >> d1 >> ad >> bd;
        cin >> s1 >> as >> bs;
        w[1] = w1;
        d[1] = d1;
        s[1] = s1;
        for(i = 2; i <= m; i++)
            w[i] = (w[i - 1] * aw + bw) % n + 1;
        for(i = 2; i <= m; i++)
            d[i] = (ad * d[i - 1] + bd) % 3;
        for(i = 1; i <= m; i++)
            z[i] = max(1LL, min(n, w[i] + d[i] - 1));
        for(i = 2; i <= m; i++)
            s[i] = (as * s[i - 1] + bs) % MOD + 1;
        build(1, 1, n);
        ll ans = 0;
        for(i = 0; i <= n + 5; i++)
        {
            g[i][same] = g[i][front] = g[i][back] = 0;
            if(i >= 1 && i <= n)
                g[i][same] = 1;
        }
        for(i = 1; i <= m; i++)
        {
            g[w[i]][z[i] - w[i] + 1] += s[i];
            if(g[w[i]][z[i] - w[i] + 1] >= mod)
                g[w[i]][z[i] - w[i] + 1] -= mod;
            upd(1, 1, n, w[i]);
            ans += tree[1];
            if(ans >= mod)
                ans -= mod;
        }
        cout << ans << endl;
    }
    return 0;
}