#include #define all(x) x.begin(), x.end() #define MOD 101ll using namespace std; using ll = long long; ll powmod(ll a, ll n) { ll ret = 1; while(n){ if(n & 1){ ret *= a; ret %= MOD; } n >>= 1; a *= a; a %= MOD; } return ret; } const ll INV6 = powmod(6, MOD - 2); ll det(vector >& P){ ll ret = 0; for(int i = 0; i < 3; ++i){ ret += P[i][0] * P[(i + 1) % 3][1] * P[(i + 2) % 3][2]; ret -= P[i][2] * P[(i + 1) % 3][1] * P[(i + 2) % 3][0]; } return ret; } int get_dp(vector > >& dp, vector& a, string& s, int i, int j, int k){ if(dp[i][j][k] == -2){ int nj = j * (a[i] + 1) % MOD, nk = k | ((a[i] + 1) % 2 == 0) | (((a[i] + 1) % 3 == 0) << 1); // cout << i << ' ' << j << ' ' << k << ' ' << nj << ' ' << nk << endl; vector results = { get_dp(dp, a, s, i + 1, j, k), get_dp(dp, a, s, i + 1, nj, nk) }; vector stat_next = (s[i] == 'K') ? vector({1, -1, 0}) : vector({0, -1, 1}); for(auto& x : stat_next){ if(find(all(results), x) == results.end()){ continue; } // cout << i << ' ' << j << ' ' << k << ' ' << x << endl; dp[i][j][k] = x; break; } } return dp[i][j][k]; } char solve(int N, int K, vector >& P, vector& a, string& s){ ll d = abs(det(P)); if(d == 0){ return 'D'; } // cout << d << ' ' << MOD << ' ' << (d % MOD * INV6 % MOD) << endl; vector > > dp(N + 1, vector >(MOD, vector(4, -2))); for(int j = 0; j < MOD; ++j){ for(int k = 0; k < 3; ++k){ dp[N][j][k] = -1; } dp[N][j][3] = (int)(j >= K); } int g = get_dp(dp, a, s, 0, (int)(d % MOD * INV6 % MOD), (d % 2 == 0) | ((d % 3 == 0) << 1)); if(g == -1){ return 'D'; } return (g == 1) ? 'K' : 'P'; } int main(){ int t; cin >> t; for(int i = 0; i < t; ++i){ int N, K; cin >> N >> K; vector > P(3, vector(3)); for(auto& v : P){ cin >> v[0] >> v[1] >> v[2]; } vector a(N); for(auto& x : a){ cin >> x; } string s; cin >> s; cout << solve(N, K, P, a, s) << endl; } return 0; }