Problem p03170 (C++)

Buggy submission (status: Runtime Error):
#include <bits/stdc++.h>            // [PRIMES]               1777 ~2^10.80
using namespace std;                //                       10333 ~2^13.33
using ll = long long;               // seq 1 128 | factor   100333 ~2^16.61
using vl = vector<ll>;              //   | grep -v ' .* '  1300111 ~2^20.31
using vvl = vector<vl>;             //                    10300777 ~2^23.30
using vb = vector<bool>;            //                   100400999 ~2^26.58
using vs = vector<string>;          //                  1300400999 ~2^30.28
using pll = pair<ll, ll>;           //                 10200500333 ~2^33.25
const ll oo = 0x3f3f3f3f3f3f3f3fLL; //                100200400777 ~2^36.54
const double eps = 1e-9;            //               1200300700111 ~2^40.13
#define sz(c) ll((c).size())        //              10200300500777 ~2^43.21
#define all(c) begin(c), end(c)     //             100200300400777 ~2^46.51
#define mp make_pair                //            1200300400600999 ~2^50.09
#define mt make_tuple               //           10200300400600111 ~2^53.18
#define pb push_back                //          100200300400600333 ~2^56.48
#define eb emplace_back             //         1200300400500800999 ~2^60.06
#define xx first
#define yy second
#define FOR(i, a, b) for (ll i = (a); i < (b); i++)
#define FORD(i, a, b) for (ll i = ll(b) - 1; i >= (a); i--)
#define TR(X)                                                                  \
  ({                                                                           \
    if (1)                                                                     \
      cerr << "TR: " << (#X) << " = " << (X) << endl;                          \
  })

using namespace std;

ll n, k;
vl values;

int dp[2][500001];

bool canWin(bool taro, ll missing) {
  if (dp[taro][missing] != -1)
    return dp[taro][missing];

  bool output;

  if (missing < values[0]) {
    output = false;
  } else {
    output = false;
    for (ll value : values) {
      if (!canWin(!taro, missing - value)) {
        output = true;
        break;
      }
    }
  }

  dp[taro][missing] = output;
  return output;
}

int main() {
  cin.sync_with_stdio(0);
  cin >> n >> k;

  FOR(i, 0, 2) {
    FOR(j, 0, 500001) { dp[i][j] = -1; }
  }

  values = vl(n);
  FOR(i, 0, k) { cin >> values[i]; }

  if (canWin(true, k))
    cout << "First" << endl;
  else
    cout << "Second" << endl;

  return 0;
}

Fixed submission:
#include <bits/stdc++.h>            // [PRIMES]               1777 ~2^10.80
using namespace std;                //                       10333 ~2^13.33
using ll = long long;               // seq 1 128 | factor   100333 ~2^16.61
using vl = vector<ll>;              //   | grep -v ' .* '  1300111 ~2^20.31
using vvl = vector<vl>;             //                    10300777 ~2^23.30
using vb = vector<bool>;            //                   100400999 ~2^26.58
using vs = vector<string>;          //                  1300400999 ~2^30.28
using pll = pair<ll, ll>;           //                 10200500333 ~2^33.25
const ll oo = 0x3f3f3f3f3f3f3f3fLL; //                100200400777 ~2^36.54
const double eps = 1e-9;            //               1200300700111 ~2^40.13
#define sz(c) ll((c).size())        //              10200300500777 ~2^43.21
#define all(c) begin(c), end(c)     //             100200300400777 ~2^46.51
#define mp make_pair                //            1200300400600999 ~2^50.09
#define mt make_tuple               //           10200300400600111 ~2^53.18
#define pb push_back                //          100200300400600333 ~2^56.48
#define eb emplace_back             //         1200300400500800999 ~2^60.06
#define xx first
#define yy second
#define FOR(i, a, b) for (ll i = (a); i < (b); i++)
#define FORD(i, a, b) for (ll i = ll(b) - 1; i >= (a); i--)
#define TR(X)                                                                  \
  ({                                                                           \
    if (1)                                                                     \
      cerr << "TR: " << (#X) << " = " << (X) << endl;                          \
  })

using namespace std;

ll n, k;
vl values;

int dp[2][500001];

bool canWin(bool taro, ll missing) {
  if (dp[taro][missing] != -1)
    return dp[taro][missing];

  bool output;

  if (missing < values[0]) {
    output = false;
  } else {
    output = false;
    for (ll value : values) {
      if (missing - value < 0)
        continue;
      if (!canWin(!taro, missing - value)) {
        output = true;
        break;
      }
    }
  }

  dp[taro][missing] = output;
  return output;
}

int main() {
  cin.sync_with_stdio(0);
  cin >> n >> k;

  FOR(i, 0, 2) {
    FOR(j, 0, 500001) { dp[i][j] = -1; }
  }

  values = vl(n);
  FOR(i, 0, k) { cin >> values[i]; }

  if (canWin(true, k))
    cout << "First" << endl;
  else
    cout << "Second" << endl;

  return 0;
}