S-nim.cpp

// iagorrr ;)
#include <bits/stdc++.h>
using namespace std;
#define endl '\n'
#define fastio                            \
        ios_base::sync_with_stdio(false); \
        cin.tie(0);                       \
        cout.tie(0);
#define rep(i, l, r) for (int i = (l); i < (r); i++)
#define len(__x) (ll) __x.size()
using ll = long long;
using vll = vector<ll>;
using pll = pair<ll, ll>;
using vll2d = vector<vll>;
using vi = vector<int>;
using pii = pair<int, int>;
using vii = vector<pii>;
using vc = vector<char>;
#define all(a) a.begin(), a.end()
#define INV(xxxx) \
        for (auto &xxx : xxxx) cin >> xxx;
#define PRINTV(___x)                                                  \
        for_each(all(___x), [](ll &____x) { cout << ____x << ' '; }), \
                cout << '\n';
#define snd second
#define fst first
#define pb(___x) push_back(___x)
#define mp(___a, ___b) make_pair(___a, ___b)
#define eb(___x) emplace_back(___x)
#define rsz(___x, ___n) resize(___x, ___n)

void dbg_out() { cerr << endl; }
template <typename H, typename... T>
void dbg_out(H h, T... t) {
        cerr << ' ' << h;
        dbg_out(t...);
}
#define dbg(...)                             \
        {                                    \
                cerr << #__VA_ARGS__ << ':'; \
                dbg_out(__VA_ARGS__);        \
        }
const ll INF = 1e18;

ll N = 10'000;
vll sg(N + 1);
void precompute(const vll &st) {
        sg[0] = 0;
        for (ll i = 1; i <= N; i++) {
                vc seen(i + 1);
                for (auto &sti : st) {
                        if (i >= sti) {
                                seen[sg[i - sti]] = true;
                        }
                }
                // find the mex
                ll curr = 0;
                while (seen[curr]) {
                        curr++;
                }
                sg[i] = curr;
        }
}
char solve(const vll &h) {
        vc seen(N);
        ll fxor(0);
        for (auto &hi : h) {
                fxor ^= sg[hi];
        }
        if (fxor == 0) return 'L';
        return 'W';
}
void run() {
        ll k;
        cin >> k;
        vll s(k);
        INV(s);
        precompute(s);

        ll n;
        cin >> n;
        for (int i = 0; i < n; i++) {
                ll m;
                cin >> m;
                vll h(m);
                INV(h);
                cout << solve(h);
        }
        cout << endl;
}
int32_t main(void) {
        // fastio;
        int t;
        t = 1;
        // cin >> t;
        while (t--) run();
}

// AC, game theory, Groundy, nim game