Problem p02851 (C++)

Buggy submission (status: Runtime Error):
// clang-format off
#include <bits/stdc++.h>
using namespace std;
#define int long long
#define stoi stoll
using pii = pair<int,int>;
using vi = vector<int>;
using vvi = vector<vi>;
#define all(c) begin(c), end(c)
#define rall(c) rbegin(c), rend(c)
#define fore(x, c) for(auto &&x : c)
#define rep(i, a, n) for(int i = a, i##len = (int)(n); i < i##len; ++i)
#define rrep(i, a, n) for(int i = (int)(n - 1); i >= a; --i)
#define sz(c) ((int)c.size())
#define contains(c, x) (c.find(x) != end(c))
#define inseg(l, x, r) ((l) <= (x) && (x) < (r))
#define dump(...)
#define pb push_back
#define eb emplace_back
#define _ 0
const signed INF_ = 1001001001; const long long INF = 1001001001001001001LL;
const int DX[9] = {0,1,0,-1,1,1,-1,-1,0}, DY[9] = {-1,0,1,0,-1,1,1,-1,0};
template<class T> ostream& operator<<(ostream &os, const vector<T> &v) {
  for (auto i = begin(v); i != end(v); i++) os<<*i<<(i==end(v)-1?"":" ");return os;}
template<class T> istream& operator>>(istream &is, vector<T> &v) {
  for (auto i = begin(v); i != end(v); i++) is>>*i;return is;}
template<class T,class U> istream& operator>>(istream &is, pair<T,U> &p) {
  is>>p.first>>p.second;return is;}
template<class T, class U> bool chmax(T &a, const U &b){return a<b?a=b,1:0;}
template<class T, class U> bool chmin(T &a, const U &b){return a>b?a=b,1:0;}
template <class T> void psum(T& c) {partial_sum(begin(c), end(c), begin(c));}
template<class T> using heap = priority_queue<T, deque<T>, greater<T>>;
struct before_main_function {
  before_main_function() {
      cin.tie(nullptr); ios::sync_with_stdio(0);
      cout << setprecision(15) << fixed;
  }
} before_main_function;
// clang-format on
//------------------8<------------------------------------8<--------------------

signed main() {
  int N, K;
  cin >> N >> K;
  vi A(N);
  cin >> A;
  vi S = A;
  psum(S);

  dump(S);

  int ans = 0;
  map<int, int> cnt;
  vi lim(N, -1);
  cnt[1] = 1;
  lim[-1 + K] = 1;
  rep(i, 0, N) {
    dump(i);
    if (lim[i] != -1) {
      dump(lim[i]);
      cnt[lim[i]]--;
    }
    int x = (S[i] - i + K) % K;
    dump(x, cnt[x]);
    ans += cnt[x];
    cnt[x]++;
    if (i + K < N)
      lim[i + K] = x;
  }
  cout << ans << endl;
  return (0 ^ _ ^ 0);
}


Fixed submission:
// clang-format off
#include <bits/stdc++.h>
using namespace std;
#define int long long
#define stoi stoll
using pii = pair<int,int>;
using vi = vector<int>;
using vvi = vector<vi>;
#define all(c) begin(c), end(c)
#define rall(c) rbegin(c), rend(c)
#define fore(x, c) for(auto &&x : c)
#define rep(i, a, n) for(int i = a, i##len = (int)(n); i < i##len; ++i)
#define rrep(i, a, n) for(int i = (int)(n - 1); i >= a; --i)
#define sz(c) ((int)c.size())
#define contains(c, x) (c.find(x) != end(c))
#define inseg(l, x, r) ((l) <= (x) && (x) < (r))
#define dump(...)
#define pb push_back
#define eb emplace_back
#define _ 0
const signed INF_ = 1001001001; const long long INF = 1001001001001001001LL;
const int DX[9] = {0,1,0,-1,1,1,-1,-1,0}, DY[9] = {-1,0,1,0,-1,1,1,-1,0};
template<class T> ostream& operator<<(ostream &os, const vector<T> &v) {
  for (auto i = begin(v); i != end(v); i++) os<<*i<<(i==end(v)-1?"":" ");return os;}
template<class T> istream& operator>>(istream &is, vector<T> &v) {
  for (auto i = begin(v); i != end(v); i++) is>>*i;return is;}
template<class T,class U> istream& operator>>(istream &is, pair<T,U> &p) {
  is>>p.first>>p.second;return is;}
template<class T, class U> bool chmax(T &a, const U &b){return a<b?a=b,1:0;}
template<class T, class U> bool chmin(T &a, const U &b){return a>b?a=b,1:0;}
template <class T> void psum(T& c) {partial_sum(begin(c), end(c), begin(c));}
template<class T> using heap = priority_queue<T, deque<T>, greater<T>>;
struct before_main_function {
  before_main_function() {
      cin.tie(nullptr); ios::sync_with_stdio(0);
      cout << setprecision(15) << fixed;
  }
} before_main_function;
// clang-format on
//------------------8<------------------------------------8<--------------------

signed main() {
  int N, K;
  cin >> N >> K;
  vi A(N);
  cin >> A;
  vi S = A;
  psum(S);

  dump(S);

  int ans = 0;
  map<int, int> cnt;
  vi lim(N, -1);
  cnt[1] = 1;
  if (-1 + K < N)
    lim[-1 + K] = 1;
  rep(i, 0, N) {
    dump(i);
    if (lim[i] != -1) {
      dump(lim[i]);
      cnt[lim[i]]--;
    }
    int x = (S[i] - i + K) % K;
    dump(x, cnt[x]);
    ans += cnt[x];
    cnt[x]++;
    if (i + K < N)
      lim[i + K] = x;
  }
  cout << ans << endl;
  return (0 ^ _ ^ 0);
}