#line 2 "/Users/noya2/Desktop/Noya2_library/template/template.hpp" using namespace std; #include #line 1 "/Users/noya2/Desktop/Noya2_library/template/inout_old.hpp" namespace noya2 { template ostream &operator<<(ostream &os, const pair &p){ os << p.first << " " << p.second; return os; } template istream &operator>>(istream &is, pair &p){ is >> p.first >> p.second; return is; } template ostream &operator<<(ostream &os, const vector &v){ int s = (int)v.size(); for (int i = 0; i < s; i++) os << (i ? " " : "") << v[i]; return os; } template istream &operator>>(istream &is, vector &v){ for (auto &x : v) is >> x; return is; } void in() {} template void in(T &t, U &...u){ cin >> t; in(u...); } void out() { cout << "\n"; } template void out(const T &t, const U &...u){ cout << t; if (sizeof...(u)) cout << sep; out(u...); } template void out(const vector> &vv){ int s = (int)vv.size(); for (int i = 0; i < s; i++) out(vv[i]); } struct IoSetup { IoSetup(){ cin.tie(nullptr); ios::sync_with_stdio(false); cout << fixed << setprecision(15); cerr << fixed << setprecision(7); } } iosetup_noya2; } // namespace noya2 #line 1 "/Users/noya2/Desktop/Noya2_library/template/const.hpp" namespace noya2{ const int iinf = 1'000'000'007; const long long linf = 2'000'000'000'000'000'000LL; const long long mod998 = 998244353; const long long mod107 = 1000000007; const long double pi = 3.14159265358979323; const vector dx = {0,1,0,-1,1,1,-1,-1}; const vector dy = {1,0,-1,0,1,-1,-1,1}; const string ALP = "ABCDEFGHIJKLMNOPQRSTUVWXYZ"; const string alp = "abcdefghijklmnopqrstuvwxyz"; const string NUM = "0123456789"; void yes(){ cout << "Yes\n"; } void no(){ cout << "No\n"; } void YES(){ cout << "YES\n"; } void NO(){ cout << "NO\n"; } void yn(bool t){ t ? yes() : no(); } void YN(bool t){ t ? YES() : NO(); } } // namespace noya2 #line 1 "/Users/noya2/Desktop/Noya2_library/template/utils.hpp" namespace noya2{ unsigned long long inner_binary_gcd(unsigned long long a, unsigned long long b){ if (a == 0 || b == 0) return a + b; int n = __builtin_ctzll(a); a >>= n; int m = __builtin_ctzll(b); b >>= m; while (a != b) { int mm = __builtin_ctzll(a - b); bool f = a > b; unsigned long long c = f ? a : b; b = f ? b : a; a = (c - b) >> mm; } return a << min(n, m); } template T gcd_fast(T a, T b){ return static_cast(inner_binary_gcd(abs(a),abs(b))); } long long sqrt_fast(long long n) { if (n <= 0) return 0; long long x = sqrt(n); while ((x + 1) * (x + 1) <= n) x++; while (x * x > n) x--; return x; } template T floor_div(const T n, const T d) { assert(d != 0); return n / d - static_cast((n ^ d) < 0 && n % d != 0); } template T ceil_div(const T n, const T d) { assert(d != 0); return n / d + static_cast((n ^ d) >= 0 && n % d != 0); } template void uniq(vector &v){ sort(v.begin(),v.end()); v.erase(unique(v.begin(),v.end()),v.end()); } template inline bool chmin(T &x, U y) { return (y < x) ? (x = y, true) : false; } template inline bool chmax(T &x, U y) { return (x < y) ? (x = y, true) : false; } template inline bool range(T l, T x, T r){ return l <= x && x < r; } } // namespace noya2 #line 8 "/Users/noya2/Desktop/Noya2_library/template/template.hpp" #define rep(i,n) for (int i = 0; i < (int)(n); i++) #define repp(i,m,n) for (int i = (m); i < (int)(n); i++) #define reb(i,n) for (int i = (int)(n-1); i >= 0; i--) #define all(v) (v).begin(),(v).end() using ll = long long; using ld = long double; using uint = unsigned int; using ull = unsigned long long; using pii = pair; using pll = pair; using pil = pair; using pli = pair; namespace noya2{ /* ~ (. _________ . /) */ } using namespace noya2; #line 2 "c.cpp" #line 2 "/Users/noya2/Desktop/Noya2_library/misc/mex.hpp" #line 4 "/Users/noya2/Desktop/Noya2_library/misc/mex.hpp" namespace noya2 { template int mex(const vector &a){ int n = a.size(); vector has(n,false); rep(i,n) if (a[i] < n) has[a[i]] = true; rep(i,n) if (!has[i]) return i; return n; } } // namespace noya2 #line 4 "c.cpp" map>,bool> mp; bool is_win(pair> mv){ if (mp.contains(mv)) return mp[mv]; bool win = false; auto [x, v] = mv; rep(i,v.size()){ for (int k = 1; k <= v[i]; k++){ if (k > x) continue; auto u = v; u[i] -= k; sort(all(u)); if (is_win({k,u})) continue; win = true; break; } } if (x == v.back()){ out(x, " # ",v,win ? "win" : "lose"); } return mp[mv] = win; } void jikken2(){ int n; in(n); vector a(n); in(a); sort(all(a)); yn(is_win({a[n-1],a})); } void jikken(){ int n, m; in(n,m); vector> dp(m,vector(n+1)); rep(i,m) rep(j,n+1){ vector a; for (int k = 1; k <= j; k++){ if ((k % m) > i) continue; a.emplace_back(dp[k%m][j-k]); } dp[i][j] = mex(a); } out(dp); } void alice(){ out("Alice"); } void bob(){ out("Bob"); } void solve(){ int n, m; in(n,m); vector a(n); in(a); int x = 0; for (auto b : a){ x ^= b/m; } if (x > 0){ alice(); return ; } set st; for (auto b : a){ b %= m; if (st.contains(b)){ st.erase(b); } else { st.insert(b); } } if (st.contains(0)){ st.erase(0); } if (st.empty()){ bob(); return ; } st.insert(0); a.clear(); for (auto b : st){ a.emplace_back(b); } n = a.size(); if (n % 4 != 0){ alice(); return ; } rep(i,n/2){ int le = a[i*2]; int ri = a[i*2+1]; if (ri - le == 1 && le % 2 == 0) continue; alice(); return ; } bob(); } int main(){ int t = 1; //in(t); while (t--) { solve(); } }