Problem p02549 (C++) — buggy submission, verdict: Time Limit Exceeded

#include <bits/stdc++.h>

using namespace std;

void __print(int x) { cerr << x; }
void __print(long x) { cerr << x; }
void __print(long long x) { cerr << x; }
void __print(unsigned x) { cerr << x; }
void __print(unsigned long x) { cerr << x; }
void __print(unsigned long long x) { cerr << x; }
void __print(float x) { cerr << x; }
void __print(double x) { cerr << x; }
void __print(long double x) { cerr << x; }
void __print(char x) { cerr << '\\'' << x << '\\''; }
void __print(const char *x) { cerr << '\\"' << x << '\\"'; }
void __print(const string &x) { cerr << '\\"' << x << '\\"'; }
void __print(bool x) { cerr << (x ? "true" : "false"); }

template <typename T, typename V> void __print(const pair<T, V> &x) {
  cerr << '{';
  __print(x.first);
  cerr << ',';
  __print(x.second);
  cerr << '}';
}
template <typename T> void __print(const T &x) {
  int f = 0;
  cerr << '{';
  for (auto &i : x)
    cerr << (f++ ? "," : ""), __print(i);
  cerr << "}";
}
void _print() { cerr << "]\\n"; }
template <typename T, typename... V> void _print(T t, V... v) {
  __print(t);
  if (sizeof...(v))
    cerr << ", ";
  _print(v...);
}
#ifndef ONLINE_JUDGE
#define debug(x...)                                                            \\
  cerr << "[" << #x << "] = [";                                                \\
  _print(x)
#else
#define debug(x...)
#endif
const long long INF = 1e18;
int md = 998244353;

int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  int n, k;
  cin >> n >> k;
  vector<int> dp(n + 3);
  vector<int> pre(n + 3);
  vector<int> l(k);
  vector<int> r(k);
  for (int i = 0; i < k; i++) {
    cin >> l[i];
    cin >> r[i];
  }
  dp[1] = 1;
  pre[1] = 1;
  for (int i = 2; i <= n; i++) {
    for (int j = 0; j < k; j++) {
      if (l[j] >= i)
        continue;
      int left = l[j];
      int right = min(i - 1, r[j]);
      int val = (pre[i - left] - pre[i - right - 1] + md) % md;
      dp[i] = (dp[i] + val) % md;
    }
    pre[i] = (pre[i - 1] % md + dp[i] % md) % md;
  }
  cout << dp[n];
  return 0;
}
// https://www.youtube.com/watch?v=ZQqccia8bVo

Error: TLE

Fixed submission:

#include <bits/stdc++.h>

using namespace std;

void __print(int x) { cerr << x; }
void __print(long x) { cerr << x; }
void __print(long long x) { cerr << x; }
void __print(unsigned x) { cerr << x; }
void __print(unsigned long x) { cerr << x; }
void __print(unsigned long long x) { cerr << x; }
void __print(float x) { cerr << x; }
void __print(double x) { cerr << x; }
void __print(long double x) { cerr << x; }
void __print(char x) { cerr << '\\'' << x << '\\''; }
void __print(const char *x) { cerr << '\\"' << x << '\\"'; }
void __print(const string &x) { cerr << '\\"' << x << '\\"'; }
void __print(bool x) { cerr << (x ? "true" : "false"); }

template <typename T, typename V> void __print(const pair<T, V> &x) {
  cerr << '{';
  __print(x.first);
  cerr << ',';
  __print(x.second);
  cerr << '}';
}
template <typename T> void __print(const T &x) {
  int f = 0;
  cerr << '{';
  for (auto &i : x)
    cerr << (f++ ? "," : ""), __print(i);
  cerr << "}";
}
void _print() { cerr << "]\\n"; }
template <typename T, typename... V> void _print(T t, V... v) {
  __print(t);
  if (sizeof...(v))
    cerr << ", ";
  _print(v...);
}
#ifndef ONLINE_JUDGE
#define debug(x...)                                                            \\
  cerr << "[" << #x << "] = [";                                                \\
  _print(x)
#else
#define debug(x...)
#endif
const long long INF = 1e18;
int md = 998244353;
int dfs(int index, set<int> &s, int n, vector<int> &dp) {
  if (index == n)
    return 1;
  if (dp[index] != -1)
    return dp[index];
  long long ans = 0LL;
  for (auto i : s) {
    if (i + index <= n) {
      ans = (ans % md + dfs(i + index, s, n, dp) % md) % md;
    }
  }
  return dp[index] = ans;
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  int n, k;
  cin >> n >> k;
  vector<int> pre(n + 2);
  for (int i = 0; i < k; i++) {
    int l, r;
    cin >> l >> r;
    pre[l]++;
    pre[r + 1]--;
  }
  // debug(pre);
  for (int i = 1; i <= n; i++) {
    pre[i] += pre[i - 1];
  }
  // debug(pre);
  set<int> s;
  for (int i = 1; i <= n; i++) {
    if (pre[i] >= 1)
      s.insert(i);
  }

  vector<int> dp(n + 1, -1);
  int ans = dfs(1, s, n, dp);
  // debug(dp);
  cout << ans;
  return 0;
}
// https://www.youtube.com/watch?v=ZQqccia8bVo