結果

問題 No.3090 NimNim
ユーザー 👑 amentorimaru
提出日時 2025-02-20 00:41:15
言語 C++23
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 70 ms / 2,000 ms
コード長 7,462 bytes
コンパイル時間 4,463 ms
コンパイル使用メモリ 268,384 KB
実行使用メモリ 7,716 KB
最終ジャッジ日時 2025-04-01 20:52:17
合計ジャッジ時間 6,693 ms
ジャッジサーバーID
（参考情報） 		judge3 / judge2
このコードへのチャレンジ
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ファイルパターン 結果
sample AC * 3
other AC * 25
権限があれば一括ダウンロードができます

ソースコード

diff # 

#define ATCODER
#define _USE_MATH_DEFINES
#include<stdio.h>
#include <bit>
#include <cstdint>
#include<iostream>
#include<fstream>
#include<algorithm>
#include<vector>
#include<string>
#include <cassert>
#include <numeric>
#include <unordered_map>
#include <unordered_set>
#include <queue>
#include <math.h>
#include <climits>
#include <set>
#include <map>
#include <list>
#include <random>
#include <iterator>
#include <bitset>
#include <chrono>
#include <type_traits>
using namespace std;

using ll = long long;
using ld = long double;
using pll = pair<ll, ll>;
using pdd = pair<ld, ld>;

//template<claLR T> using pq = priority_queue<T, vector<T>, greater<T>>;

#define FOR(i, a, b) for(ll i=(a); i<(b);i++)
#define REP(i, n) for(ll i=0; i<(n);i++)
#define ROF(i, a, b) for(ll i=(b-1); i>=(a);i--)
#define PER(i, n) for(ll i=n-1; i>=0;i--)
#define REPREP(i,j,a,b) for(ll i=0;i<a;i++)for(ll j=0;j<b;j++)
#define VV(type) vector< vector<type> >
#define VV2(type,n,m,val) vector< vector<type> > val;val.resize(n);for(ll i;i<n;i++)val[i].resize(m)
#define vec(type) vector<type>
#define VEC(type,n,val) vector<type> val;val.resize(n)
#define VL vector<ll>
#define VVL vector< vector<ll> >
#define VP vector< pair<ll,ll> >
#define SZ size()
#define all(i) begin(i),end(i)
#define SORT(i) sort(all(i))
#define BITI(i) (1<<i)
#define BITSET(x,i) x | (ll(1)<<i)
#define BITCUT(x,i) x & ~(ll(1)<<i)
#define EXISTBIT(x,i) (((x>>i) & 1) != 0)
#define ALLBIT(n) (ll(1)<<n-1)
#define CHMAX(n,v) n=n<v?v:n
#define CHMIN(n,v) n=n>v?v:n
#define MP(a,b) make_pair(a,b)
#define DET2(x1,y1,x2,y2) (x1)*(y2)-(x2)*(y1)
#define DET3(x1,y1,z1,x2,y2,z2,x3,y3,z3) (x1)*(y2)*(z3)+(x2)*(y3)*(z1)+(x3)*(y1)*(z2)-(z1)*(y2)*(x3)-(z2)*(y3)*(x1)-(z3)*(y1)*(x2)
#define INC(a) for(auto& v:a)v++;
#define DEC(a) for(auto& v:a)v--;
#define SQU(x) (x)*(x)
#define L0 ll(0)
#ifdef ATCODER
#include <atcoder/all>
using namespace atcoder;
//using mint = modint1000000007;
using mint2 = modint998244353;
#endif
template<typename T = ll>
vector<T> read(size_t n) {
  vector<T> ts(n);
  for (size_t i = 0; i < n; i++) cin >> ts[i];
  return ts;
}

template<typename TV, const ll N> void read_tuple_impl(TV&) {}
template<typename TV, const ll N, typename Head, typename... Tail>
void read_tuple_impl(TV& ts) {
  get<N>(ts).emplace_back(*(istream_iterator<Head>(cin)));
  read_tuple_impl<TV, N + 1, Tail...>(ts);
}
template<typename... Ts> decltype(auto) read_tuple(size_t n) {
  tuple<vector<Ts>...> ts;
  for (size_t i = 0; i < n; i++) read_tuple_impl<decltype(ts), 0, Ts...>(ts);
  return ts;
}

using val = ll;
using func = ll;

val op(val a, val b) {
  return a + b;
}


val e() { return 0; }

val mp(func f, val a)
{
  return a + f;
}
func comp(func f, func g) {
  return f + g;
}

func id() {
  return 0;
}

ll g;
bool f(val a) {
  return a < g;
}

ll di[4] = { 1,0,-1,0 };
ll dj[4] = { 0,1,0,-1 };
ll si[4] = { 0,3,3,0 };
ll sj[4] = { 0,0,3,3 };
//ll di[4] = { -1,-1,1,1 };
//ll dj[4] = { -1,1,-1,1 };
//ll di8[8] = { 0,-1,-1,-1,0,1,1,1 };
//ll dj8[8] = { -1,-1,0,1,1,1,0,-1 };

class Rational {
public:
  Rational(ll nn = 0, ll dd = 1) {
    n = nn; d = dd; Reduction();
  }
  Rational operator+() const { return *this; }

  Rational& operator=(ll nn) { n = nn; d = 1; return *this; }
  Rational& operator = (const Rational& r) { n = r.n; d = r.d; return *this; }
  Rational& operator += (const Rational& r) { n = n * r.d + r.n * d; d *= r.d; Reduction(); return *this; }
  Rational& operator -= (const Rational& r) { n = n * r.d - r.n * d; d *= r.d; Reduction(); return *this; }
  Rational& operator *= (const Rational& r) { n *= r.n; d *= r.d; Reduction();  return *this; }
  Rational& operator /= (const Rational& r) { n *= r.d; d *= r.n; Reduction();  return *this; }

  bool operator ==(const Rational& r) { return n * r.d == r.n * d; }
  bool operator !=(const Rational& r) { return !(*this == r); }
  bool operator <(const Rational& r) {
    if (d == 0 && r.d == 0) return n < 0 && 0 < r.n;
    if (r.d == 0) return r.n > 0;
    if (d == 0) return n < 0;
    return n * r.d < r.n * d;
  }
  bool operator >(const Rational& r) {
    if (d == 0 && r.d == 0) return r.n < 0 && 0 < n;
    if (r.d == 0) return r.n < 0;
    if (d == 0) return n > 0;
    return n * r.d < r.n * d;
  }

  bool operator <=(const Rational& r) { return !(*this > r); }
  bool operator >=(const Rational& r) { return !(*this < r); }

  void Reduction() {
    ll g = gcd(n, d);
    if (g == 0)return;
    if (d < 0)g *= -1;
    n /= g; d /= g;
  }
  // d is not negative
  ll n, d;
};

static Rational operator + (const Rational& l, const Rational& r) { return Rational(l) += r; }
static Rational operator - (const Rational& l, const Rational& r) { return Rational(l) -= r; }
static Rational operator * (const Rational& l, const Rational& r) { return Rational(l) *= r; }
static Rational operator / (const Rational& l, const Rational& r) { return Rational(l) /= r; }
static bool operator < (const Rational& l, const Rational& r) { return Rational(l) < r; }
static bool operator > (const Rational& l, const Rational& r) { return Rational(l) > r; }
static bool operator <= (const Rational& l, const Rational& r) { return Rational(l) <= r; }
static bool operator >= (const Rational& l, const Rational& r) { return Rational(l) >= r; }


void solve() {
  ll n;
  ll m;
  cin >> n >> m;
  VL a = read(n);
  VL b = read(m);
  ll xa = 0;
  ll mx = 0;
  REP(i, n) {
    xa ^= a[i];
    CHMAX(mx, a[i]);
  }

  // 先手が逆Nimに勝てるなら後手に一方的に取らせ続けられるんだったらそれでよい
  if ((mx == 1 && xa != 1) || (mx != 1 && xa != 0)) {    
    cout << "First";
  }
  else {
    //1が奇数個あるだけの山だったら、普通にBのNimになる 
    if (mx == 1) {
      ll xb = 0;
      REP(i, m)
        xb ^= b[i];
      if (xb) {
        cout << "First";
      }
      else {
        cout << "Second";
      }
    }
    // xorが0なら後手は通常Nimで勝ち続けBをまっさらにした後に、最後に逆Nimで勝てばよい
    else {
      cout << "Second";
    }
  }


  //map<pair<VL, VL>, ll> grundy;
  //VL ea(n), eb(m);
  //grundy[MP(ea, eb)] = 99;
  //REP(i, n) {
  //  ea[i] = 1;
  //  grundy[MP(ea, eb)] = 0;
  //  ea[i] = 0;
  //}

  //auto dfs = [&](auto self, VL& aa, VL& bb)->ll {
  //  if (grundy.find(MP(aa, bb)) != grundy.end()) {
  //    return grundy[MP(aa, bb)];
  //  }
  //  vector<bool> ff(100);
  //  ll acnt = 0;
  //  REP(i, n) {
  //    acnt += aa[i] > 0;
  //  }
  //  REP(i, n) {
  //    REP(j, aa[i]) {
  //      if (j == aa[i] - 1 && acnt == 1)
  //        break;
  //      aa[i] -= j + 1;
  //      ll res = self(self, aa, bb);
  //      ff[res] = true;
  //      aa[i] += j + 1;
  //    }
  //  }
  //  if (acnt == 1) {
  //    ll bcnt = 0;
  //    REP(i, m) {
  //      bcnt += b[i] > 0;
  //    }
  //    if (bcnt != 0) {
  //      REP(i, m) {
  //        REP(j, bb[i]) {
  //          bb[i] -= j + 1;
  //          VL na = a;
  //          ll res = self(self, na, bb);
  //          ff[res] = true;
  //          bb[i] += j + 1;
  //        }
  //      }
  //    }
  //  }
  //  ll gg = 0;
  //  while (ff[gg]) {
  //    gg++;
  //  }
  //  return grundy[MP(aa, bb)] = gg;
  //};
  //VL aaa = a;
  //VL bbb = b;
  //ll r = dfs(dfs, aaa, bbb);
  //if (r) {
  //  cout << "First";
  //}
  //else {
  //  cout << "Second";
  //}
  return;
}

int main() {
  ll t = 1;
  //cin >> t;
  while (t--) {
    solve();
  }
  return 0;
}
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