Problem p03128 (C++)

Buggy submission (status: Runtime Error):
// includes
#include <algorithm>
#include <bitset>
#include <climits>
#include <cmath>
#include <cstdint>
#include <cstdio>
#include <functional>
#include <iomanip>
#include <iostream>
#include <list>
#include <map>
#include <queue>
#include <random>
#include <set>
#include <stack>
#include <string>
#include <unordered_map>
#include <utility>
#include <vector>

// macros
#define ll long long int
#define pb emplace_back
#define mk make_pair
#define pq priority_queue
#define FOR(i, a, b) for (int i = (a); i < (b); ++i)
#define rep(i, n) FOR(i, 0, n)
#define rrep(i, n) for (int i = ((int)(n)-1); i >= 0; i--)
#define all(x) (x).begin(), (x).end()
#define sz(x) ((int)(x).size())
#define UNIQUE(v) v.erase(unique(v.begin(), v.end()), v.end())

using namespace std;

//  types
typedef pair<int, int> P;
typedef pair<ll, int> Pl;
typedef pair<ll, ll> Pll;
typedef pair<double, double> Pd;

// constants
const int inf = 1e9;
const ll linf = 1LL << 50;
const double EPS = 1e-10;
const int mod = 1e9 + 7;

// solve
template <class T> bool chmax(T &a, const T &b) {
  if (a < b) {
    a = b;
    return 1;
  }
  return 0;
}
template <class T> bool chmin(T &a, const T &b) {
  if (a > b) {
    a = b;
    return 1;
  }
  return 0;
}

int ma[9] = {2, 5, 5, 4, 5, 6, 3, 7, 6};

string maxs(string a, string b) {
  if (a == "a")
    return b;
  if (b == "a")
    return a;
  if (a.size() != b.size()) {
    if (a.size() > b.size())
      return a;
    else
      return b;
  }
  for (int i = 0; i < sz(a); i++) {
    if (a[i] != b[i]) {
      if (a[i] < b[i])
        return b;
      else
        return a;
    }
  }
  return a;
}

int main(int argc, char const *argv[]) {
  int n, m;
  cin >> n >> m;
  vector<string> dp;
  for (int i = 0; i <= 1001; i++)
    dp.pb("a");
  vector<int> a(m);
  rep(i, m) cin >> a[i];
  rep(i, m) { dp[ma[a[i] - 1]] = maxs(dp[ma[a[i] - 1]], to_string(a[i])); }
  dp[0] = "";
  for (int i = 1; i <= n; i++) {
    for (int j = 0; j < m; j++) {
      if (i - ma[a[j] - 1] >= 0 && dp[i - ma[a[j] - 1]] != "a") {
        dp[i] = maxs(dp[i], dp[i - ma[a[j] - 1]] + to_string(a[j]));
      }
    }
  }
  cout << dp[n] << endl;
  return 0;
}


Fixed submission:
// includes
#include <algorithm>
#include <bitset>
#include <climits>
#include <cmath>
#include <cstdint>
#include <cstdio>
#include <functional>
#include <iomanip>
#include <iostream>
#include <list>
#include <map>
#include <queue>
#include <random>
#include <set>
#include <stack>
#include <string>
#include <unordered_map>
#include <utility>
#include <vector>

// macros
#define ll long long int
#define pb emplace_back
#define mk make_pair
#define pq priority_queue
#define FOR(i, a, b) for (int i = (a); i < (b); ++i)
#define rep(i, n) FOR(i, 0, n)
#define rrep(i, n) for (int i = ((int)(n)-1); i >= 0; i--)
#define all(x) (x).begin(), (x).end()
#define sz(x) ((int)(x).size())
#define UNIQUE(v) v.erase(unique(v.begin(), v.end()), v.end())

using namespace std;

//  types
typedef pair<int, int> P;
typedef pair<ll, int> Pl;
typedef pair<ll, ll> Pll;
typedef pair<double, double> Pd;

// constants
const int inf = 1e9;
const ll linf = 1LL << 50;
const double EPS = 1e-10;
const int mod = 1e9 + 7;

// solve
template <class T> bool chmax(T &a, const T &b) {
  if (a < b) {
    a = b;
    return 1;
  }
  return 0;
}
template <class T> bool chmin(T &a, const T &b) {
  if (a > b) {
    a = b;
    return 1;
  }
  return 0;
}

int ma[9] = {2, 5, 5, 4, 5, 6, 3, 7, 6};

string maxs(string a, string b) {
  if (a == "a")
    return b;
  if (b == "a")
    return a;
  if (a.size() != b.size()) {
    if (a.size() > b.size())
      return a;
    else
      return b;
  }
  for (int i = 0; i < sz(a); i++) {
    if (a[i] != b[i]) {
      if (a[i] < b[i])
        return b;
      else
        return a;
    }
  }
  return a;
}

int main(int argc, char const *argv[]) {
  int n, m;
  cin >> n >> m;
  vector<string> dp;
  for (int i = 0; i <= 10001; i++)
    dp.pb("a");
  vector<int> a(m);
  rep(i, m) cin >> a[i];
  rep(i, m) { dp[ma[a[i] - 1]] = maxs(dp[ma[a[i] - 1]], to_string(a[i])); }
  dp[0] = "";
  for (int i = 1; i <= n; i++) {
    for (int j = 0; j < m; j++) {
      if (i - ma[a[j] - 1] >= 0 && dp[i - ma[a[j] - 1]] != "a") {
        dp[i] = maxs(dp[i], dp[i - ma[a[j] - 1]] + to_string(a[j]));
      }
    }
  }
  cout << dp[n] << endl;
  return 0;
}