Problem p00460 (C++) — buggy submission, verdict: Time Limit Exceeded

#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using ull = unsigned long long;

#define REP(i, n) for (long long i = 0; i < (n); i++)
#define FOR(i, m, n) for (long long i = (m); i < (n); ++i)
#define ALL(obj) (obj).begin(), (obj).end()

template <class T> using V = vector<T>;
template <class T, class U> using P = pair<T, U>;

const ll MOD = (ll)1e9 + 7;
const ll MOD2 = 998244353;
const ll LLINF = (ll)1e18;
const ll INTINF = (ll)1e9;
const long double PI = 3.1415926535897932384626433;

template <typename T> vector<T> make_v(size_t a, T b) {
  return vector<T>(a, b);
}
template <typename... Ts> auto make_v(size_t a, Ts... ts) {
  return vector<decltype(make_v(ts...))>(a, make_v(ts...));
}
template <class T> void corner(bool flg, T hoge) {
  if (flg) {
    cout << hoge << endl;
    exit(0);
  }
}
template <class T, class U>
ostream &operator<<(ostream &o, const map<T, U> &obj) {
  o << "{";
  for (auto &x : obj)
    o << " {" << x.first << " : " << x.second << "}"
      << ",";
  o << " }";
  return o;
}
template <class T> ostream &operator<<(ostream &o, const set<T> &obj) {
  o << "{";
  for (auto itr = obj.begin(); itr != obj.end(); ++itr)
    o << (itr != obj.begin() ? ", " : "") << *itr;
  o << "}";
  return o;
}
template <class T> ostream &operator<<(ostream &o, const vector<T> &obj) {
  o << "{";
  for (int i = 0; i < (int)obj.size(); ++i)
    o << (i > 0 ? ", " : "") << obj[i];
  o << "}";
  return o;
}
template <class T, class U>
ostream &operator<<(ostream &o, const pair<T, U> &obj) {
  o << "{" << obj.first << ", " << obj.second << "}";
  return o;
}
template <template <class tmp> class T, class U>
ostream &operator<<(ostream &o, const T<U> &obj) {
  o << "{";
  for (auto itr = obj.begin(); itr != obj.end(); ++itr)
    o << (itr != obj.begin() ? ", " : "") << *itr;
  o << "}";
  return o;
}
void print(void) { cout << endl; }
template <class Head> void print(Head &&head) {
  cout << head;
  print();
}
template <class Head, class... Tail> void print(Head &&head, Tail &&...tail) {
  cout << head << " ";
  print(forward<Tail>(tail)...);
}
template <class T> void chmax(T &a, const T b) { a = max<T>(a, b); }
template <class T> void chmin(T &a, const T b) { a = min<T>(a, b); }
void YN(bool flg) { cout << ((flg) ? "YES" : "NO") << endl; }
void Yn(bool flg) { cout << ((flg) ? "Yes" : "No") << endl; }
void yn(bool flg) { cout << ((flg) ? "yes" : "no") << endl; }

int main() {
  while (1) {
    int N, M, S;
    cin >> N >> M >> S;
    if (N == 0 && M == 0 && S == 0)
      return 0;
    N *= N;
    N += 1;
    S += 1;
    auto dp = make_v(N * S, 0);
    dp[0] = 1;
    for (int i = 0; i < M; ++i) {
      auto tmp = make_v(N * S, 0);
      for (int j = 0; j < N; ++j) {
        if (j + 1 < N)
          for (int k = 0; k < S; ++k) {
            if (k + i + 1 < S)
              tmp[(j + 1) * S + k + (i + 1)] += dp[j * S + k];
            else
              break;
          }
        for (int k = 0; k < S; ++k) {
          (tmp[j * S + k] += dp[j * S + k]) %= 100000LL;
        }
      }
      dp = tmp;
    }
    cout << dp[N * S - 1] << endl;
  }

  return 0;
}


Error: TLE

Fixed submission:

#include <algorithm>
#include <iostream>
#include <map>
#include <queue>
#include <set>
#include <vector>

using namespace std;
using ll = long long;
using ull = unsigned long long;

#define REP(i, n) for (long long i = 0; i < (n); i++)
#define FOR(i, m, n) for (long long i = (m); i < (n); ++i)
#define ALL(obj) (obj).begin(), (obj).end()
#define SPEED                                                                  \\
  cin.tie(0);                                                                  \\
  ios::sync_with_stdio(false);

template <class T> using V = vector<T>;
template <class T, class U> using P = pair<T, U>;

const ll MOD = (ll)1e9 + 7;
const ll MOD2 = 998244353;
const ll HIGHINF = (ll)1e18;
const ll LOWINF = (ll)1e15;
const long double PI = 3.1415926535897932384626433;

template <class T> void corner(bool flg, T hoge) {
  if (flg) {
    cout << hoge << endl;
    exit(0);
  }
}
template <class T, class U>
ostream &operator<<(ostream &o, const map<T, U> &obj) {
  o << "{";
  for (auto &x : obj)
    o << " {" << x.first << " : " << x.second << "}"
      << ",";
  o << " }";
  return o;
}
template <class T> ostream &operator<<(ostream &o, const set<T> &obj) {
  o << "{";
  for (auto itr = obj.begin(); itr != obj.end(); ++itr)
    o << (itr != obj.begin() ? ", " : "") << *itr;
  o << "}";
  return o;
}
template <class T> ostream &operator<<(ostream &o, const multiset<T> &obj) {
  o << "{";
  for (auto itr = obj.begin(); itr != obj.end(); ++itr)
    o << (itr != obj.begin() ? ", " : "") << *itr;
  o << "}";
  return o;
}
template <class T> ostream &operator<<(ostream &o, const vector<T> &obj) {
  o << "{";
  for (int i = 0; i < (int)obj.size(); ++i)
    o << (i > 0 ? ", " : "") << obj[i];
  o << "}";
  return o;
}
template <class T, class U>
ostream &operator<<(ostream &o, const pair<T, U> &obj) {
  o << "{" << obj.first << ", " << obj.second << "}";
  return o;
}
template <template <class tmp> class T, class U>
ostream &operator<<(ostream &o, const T<U> &obj) {
  o << "{";
  for (auto itr = obj.begin(); itr != obj.end(); ++itr)
    o << (itr != obj.begin() ? ", " : "") << *itr;
  o << "}";
  return o;
}
void print(void) { cout << endl; }
template <class Head> void print(Head &&head) {
  cout << head;
  print();
}
template <class Head, class... Tail> void print(Head &&head, Tail &&...tail) {
  cout << head << " ";
  print(forward<Tail>(tail)...);
}
template <class T> void chmax(T &a, const T b) { a = max<T>(a, b); }
template <class T> void chmin(T &a, const T b) { a = min<T>(a, b); }
void YN(bool flg) { cout << ((flg) ? "YES" : "NO") << endl; }
void Yn(bool flg) { cout << ((flg) ? "Yes" : "No") << endl; }
void yn(bool flg) { cout << ((flg) ? "yes" : "no") << endl; }

int main() {
  while (1) {
    ll N, M, S;
    cin >> N >> M >> S;
    if (N == 0 && M == 0 && S == 0)
      return 0;
    N = N * N;
    V<V<ll>> dp(N + 1, V<ll>(S + 1, 0));
    dp[0][0] = 1;
    for (int i = 0; i < M; ++i) {
      V<V<ll>> tmp(N + 1, V<ll>(S + 1, 0));
      for (int j = 0; j < N + 1; ++j) {
        for (int k = 0; k < S + 1; ++k) {
          if (j + 1 <= N && k + i + 1 <= S)
            (tmp[j + 1][k + (i + 1)] += dp[j][k]) %= 100000LL;
          else
            break;
        }
        for (int k = 0; k < S + 1; ++k) {
          (tmp[j][k] += dp[j][k]) %= 100000LL;
        }
      }
      dp = tmp;
    }
    cout << dp[N][S] << endl;
  }
  return 0;
}