Problem p02708 (C++) — buggy submission, verdict: Time Limit Exceeded

#include <algorithm>
#include <complex>
#include <functional>
#include <iomanip>
#include <iostream>
#include <map>
#include <math.h>
#include <queue>
#include <set>
#include <stack>
#include <stdio.h>
#include <string.h>
#include <string>
#include <time.h>
#include <vector>
using namespace std;
#define rep(i, a, n) for (int i = (a); i < (n); i++)
#define ll long long
#define llint long long int
#define reverse(v) reverse(v.begin(), v.end());
#define Yes(ans)                                                               \\
  if (ans)                                                                     \\
    cout << "Yes" << endl;                                                     \\
  else                                                                         \\
    cout << "No" << endl;
#define YES(ans)                                                               \\
  if (ans)                                                                     \\
    cout << "YES" << endl;                                                     \\
  else                                                                         \\
    cout << "NO" << endl;
#define hei(a) vector<a>
#define whei(a) vector<vector<a>>
#define UF UnionFind
#define Pint pair<int, int>
#define keta(a) fixed << setprecision(a)
constexpr auto INF = 1000000000000000000;
constexpr auto mod = 1000000007;
// 辞書順はnext_permutation( begin( v ), end( v ) );やで！
struct edge {
  int to, cost;
};

ll gcd(ll a, ll b) {
  if (a < b)
    swap(a, b);
  if (b == 0)
    return a;
  return gcd(b, a % b);
}

long long modpow(long long a, long long n, long long mod) {
  long long res = 1;
  while (n > 0) {
    if (n & 1)
      res = res * a % mod;
    a = a * a % mod;
    n >>= 1;
  }
  return res;
}

// mod. m での a の逆元 a^{-1} を計算するよ！
long long modinv(long long a, long long m) {
  long long b = m, u = 1, v = 0;
  while (b) {
    long long t = a / b;
    a -= t * b;
    swap(a, b);
    u -= t * v;
    swap(u, v);
  }
  u %= m;
  if (u < 0)
    u += m;
  return u;
}

// aCbをmod.mで割った余りを求める
ll int c(ll int a, ll int b, ll int m) {
  ll int ans = 1;
  for (ll int i = 0; i < b; i++) {
    ans *= a - i;
    ans %= m;
  }
  for (ll int i = 1; i <= b; i++) {
    ans *= modinv(i, m);
    ans %= m;
  }
  return ans;
}
struct UnionFind {
  vector<int> par; // par[i]:iの親の番号　(例) par[3] = 2 : 3の親が2

  UnionFind(int N) : par(N) { // 最初は全てが根であるとして初期化
    for (int i = 0; i < N; i++)
      par[i] = i;
  }
  int size(int a) { return par[root(a)]; }

  int root(int x) { // データxが属する木の根を再帰で得る：root(x) = {xの木の根}
    if (par[x] == x)
      return x;
    return par[x] = root(par[x]);
  }

  void unite(int x, int y) { // xとyの木を併合
    int rx = root(x);        // xの根をrx
    int ry = root(y);        // yの根をry
    if (rx == ry)
      return; // xとyの根が同じ(=同じ木にある)時はそのまま
    par[rx] =
        ry; // xとyの根が同じでない(=同じ木にない)時：xの根rxをyの根ryにつける
  }

  bool same(int x, int y) { // 2つのデータx, yが属する木が同じならtrueを返す
    int rx = root(x);
    int ry = root(y);
    return rx == ry;
  }
};

int main() {
  int n, k;
  cin >> n >> k;
  hei(llint) a(n + 1, 0);
  rep(i, 1, n + 1) a[i] = i + a[i - 1];
  llint ans = 0;
  rep(i, k, n + 2) {
    llint x = a[i - 1];
    llint y = a[n] - a[max(n - i, 0)];
    ans += (y - x + 1) % mod;
    ans %= mod;
  }
  cout << ans << endl;
  return 0;
}

Error: TLE

Fixed submission:

#include <algorithm>
#include <complex>
#include <functional>
#include <iomanip>
#include <iostream>
#include <map>
#include <math.h>
#include <queue>
#include <set>
#include <stack>
#include <stdio.h>
#include <string.h>
#include <string>
#include <time.h>
#include <vector>
using namespace std;
#define rep(i, a, n) for (int i = (a); i < (n); i++)
#define ll long long
#define llint long long int
#define reverse(v) reverse(v.begin(), v.end());
#define Yes(ans)                                                               \\
  if (ans)                                                                     \\
    cout << "Yes" << endl;                                                     \\
  else                                                                         \\
    cout << "No" << endl;
#define YES(ans)                                                               \\
  if (ans)                                                                     \\
    cout << "YES" << endl;                                                     \\
  else                                                                         \\
    cout << "NO" << endl;
#define hei(a) vector<a>
#define whei(a) vector<vector<a>>
#define UF UnionFind
#define rt                                                                     \\
  (a);                                                                         \\
  return (a);
#define Pint pair<int, int>
#define keta(a) fixed << setprecision(a)
constexpr auto INF = 1000000000;
constexpr auto mod = 1000000007;
// 辞書順はnext_permutation( begin( v ), end( v ) );やで！
llint gcd(llint a, llint b) {
  if (b > a)
    swap(a, b);
  if (a % b == 0)
    return b;
  return gcd(b, a % b);
}
llint Tow(int n) { // 2のn乗
  if (n == 0)
    return 1;
  llint x = Tow(n / 2);
  x %= mod;
  x *= x;
  x %= mod;
  if (n % 2 == 1)
    x *= 10;
  x %= mod;
  return x;
}

int main() {
  int n, k;
  cin >> n >> k;
  int ans = 0;
  map<ll, int> S;
  stack<string> st;
  st.push("");
  while (!st.empty()) {
    string now = st.top();
    st.pop();
    if (now.size() == n + 1) {
      int sum = 0, x = 0;
      rep(i, 0, n + 1) {
        if (now[i] == '1') {
          sum += i;
          x++;
        }
      }
      if (S[sum + (x * 100000000000)] == 0 && x >= k) {
        ans++;
        ans %= mod;
        S[sum + (x * 100000000000)] = 1;
      }

    } else {
      for (int i = 2 - 1; i >= 0; i--) {
        string next = now + to_string(i);
        st.push(next);
      }
    }
  }
  cout << ans << endl;
  return 0;
}