Problem p03172 (C++)

Buggy submission (status: Runtime Error):
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using ld = long double;
using vl = vector<ll>;
template <class T> using vc = vector<T>;
template <class T> using vvc = vector<vector<T>>;

#define eb emplace_back
#define all(x) (x).begin(), (x).end()
#define rep(i, n) for (ll i = 0; i < (n); i++)
#define repr(i, n) for (ll i = (n)-1; i >= 0; i--)
#define repe(i, l, r) for (ll i = (l); i < (r); i++)
#define reper(i, l, r) for (ll i = (r)-1; i >= (l); i--)
#define repa(i, n) for (auto &i : n)

template <class T> inline bool chmax(T &a, const T &b) {
  if (a < b) {
    a = b;
    return 1;
  }
  return 0;
}
template <class T> inline bool chmin(T &a, const T &b) {
  if (b < a) {
    a = b;
    return 1;
  }
  return 0;
}
void init() {
  cin.tie(0);
  ios::sync_with_stdio(false);
  cout << fixed << setprecision(15);
}

#ifdef DEBUG
template <class T, class N> void verr(const T &a, const N &n) {
  rep(i, n) cerr << a[i] << " ";
  cerr << "\n" << flush;
}
ll dbgt = 1;
void err() { cerr << "passed " << dbgt++ << "\n" << flush; }
template <class H, class... T> void err(H &&h, T &&...t) {
  cerr << h << (sizeof...(t) ? " " : "\n") << flush;
  if (sizeof...(t) > 0)
    err(forward<T>(t)...);
}
#endif

const ll INF = 5e18;
const ld EPS = 1e-11;
const ld PI = acos(-1.0L);
const ll MOD = 1e9 + 7;
// const ll MOD = 998244353;
//--------------------------------------------------------------------------------//
ll A[100];
ll dp[101][100005];
int main() {
  init();
  ll N, K;
  cin >> N >> K;
  rep(i, N) cin >> A[i];

  ll sum = 0;
  dp[0][0] = 1;
  rep(i, N) {
    sum += A[i];
    rep(j, sum)(dp[i][j + 1] += dp[i][j]) %= MOD;
    rep(j, sum + 1) {
      if (j - A[i] <= 0)
        dp[i + 1][j] = dp[i][j];
      else
        (dp[i + 1][j] = dp[i][j] - dp[i][j - A[i] - 1] + MOD) %= MOD;
    }
  }

  cout << dp[N][K] << endl;
}

Fixed submission:
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using ld = long double;
using vl = vector<ll>;
template <class T> using vc = vector<T>;
template <class T> using vvc = vector<vector<T>>;

#define eb emplace_back
#define all(x) (x).begin(), (x).end()
#define rep(i, n) for (ll i = 0; i < (n); i++)
#define repr(i, n) for (ll i = (n)-1; i >= 0; i--)
#define repe(i, l, r) for (ll i = (l); i < (r); i++)
#define reper(i, l, r) for (ll i = (r)-1; i >= (l); i--)
#define repa(i, n) for (auto &i : n)

template <class T> inline bool chmax(T &a, const T &b) {
  if (a < b) {
    a = b;
    return 1;
  }
  return 0;
}
template <class T> inline bool chmin(T &a, const T &b) {
  if (b < a) {
    a = b;
    return 1;
  }
  return 0;
}
void init() {
  cin.tie(0);
  ios::sync_with_stdio(false);
  cout << fixed << setprecision(15);
}

#ifdef DEBUG
template <class T, class N> void verr(const T &a, const N &n) {
  rep(i, n) cerr << a[i] << " ";
  cerr << "\n" << flush;
}
ll dbgt = 1;
void err() { cerr << "passed " << dbgt++ << "\n" << flush; }
template <class H, class... T> void err(H &&h, T &&...t) {
  cerr << h << (sizeof...(t) ? " " : "\n") << flush;
  if (sizeof...(t) > 0)
    err(forward<T>(t)...);
}
#endif

const ll INF = 5e18;
const ld EPS = 1e-11;
const ld PI = acos(-1.0L);
const ll MOD = 1e9 + 7;
// const ll MOD = 998244353;
//--------------------------------------------------------------------------------//
ll A[100];
ll dp[101][100005];
int main() {
  init();
  ll N, K;
  cin >> N >> K;
  rep(i, N) cin >> A[i];

  ll sum = 0;
  dp[0][0] = 1;
  rep(i, N) {
    sum = min(sum + A[i], K);
    rep(j, sum)(dp[i][j + 1] += dp[i][j]) %= MOD;
    rep(j, sum + 1) {
      if (j - A[i] <= 0)
        dp[i + 1][j] = dp[i][j];
      else
        (dp[i + 1][j] = dp[i][j] - dp[i][j - A[i] - 1] + MOD) %= MOD;
    }
  }

  cout << dp[N][K] << endl;
}