Problem p03172 (C++)

Buggy submission (status: Runtime Error):
#include <algorithm>
#include <cassert>
#include <cmath>
#include <deque>
#include <fstream>
#include <iomanip>
#include <iostream>
#include <map>
#include <numeric>
#include <queue>
#include <set>
#include <sstream>
#include <stack>
#include <string>
#include <unistd.h>
#include <unordered_map>
#include <vector>
using namespace std;
typedef long long ll;
typedef vector<int> vi;
typedef vector<ll> vl;
typedef vector<vl> vvl;
typedef vector<vvl> vvvl;
typedef vector<vi> vvi;
typedef vector<vvi> vvvi;
typedef vector<bool> vb;
typedef vector<vector<bool>> vvb;
typedef vector<string> vs;
typedef vector<vector<string>> vvs;
typedef vector<char> vc;
typedef vector<vector<char>> vvc;
typedef vector<double> vd;
typedef vector<vd> vvd;
typedef vector<vvd> vvvd;
typedef pair<int, int> P;
typedef pair<ll, ll> PL;
typedef vector<P> vp;
typedef vector<PL> vpl;
typedef vector<vector<P>> vvp;
typedef vector<vector<PL>> vvpl;
const int INF = 1001001001;
const ll LINF = 1e12;
const double pi = 3.1415926535897932;
const string endstr = "\n";
#define FOR(i, a, b) for (ll i = (a); i < b; i++)
#define REP(i, n) for (ll i = 0; i < n; i++)
#define FORMAP(it, m) for (auto it = m.begin(); it != m.end(); it++)
#define ff first
#define ss second
#define pb push_back

template <typename T> T gcd(T a, T b) { return (a == 0) ? b : gcd(b % a, a); }
template <typename T> T lcm(T a, T b) { return a / gcd(a, b) * b; }

bool p_comp_fs(const PL p1, const PL p2) { return p1.first < p2.first; };
bool p_comp_fg(const PL p1, const PL p2) { return p1.first > p2.first; };
bool p_comp_ss(const PL p1, const PL p2) { return p1.second < p2.second; };
bool p_comp_sg(const PL p1, const PL p2) { return p1.second > p2.second; };
template <typename T> vector<T> uniquen(vector<T> vec) {
  vec.erase(unique(vec.begin(), vec.end()), vec.end());
  return vec;
}

const ll mod = 1e9 + 7;

int main() {
  ll N, K;
  cin >> N >> K;
  vl a(N);
  REP(i, N) cin >> a[i];

  vvl dp(N + 1, vl(K + 1, 0));
  REP(i, K + 1) if (i <= a[0]) dp[1][i] = 1;
  FOR(i, 1, N) {
    vl sum(K + 1, 0);
    REP(j, K + 1) sum[j + 1] = (sum[j] + dp[i][j]) % mod;
    REP(l, K + 1) {
      dp[i + 1][l] = (sum[l + 1] - sum[max(l - a[i], 0ll)] + mod) % mod;
    }
  }
  cout << dp[N][K] % mod << endl;
  return 0;
}


Fixed submission:
#include <algorithm>
#include <cassert>
#include <cmath>
#include <deque>
#include <fstream>
#include <iomanip>
#include <iostream>
#include <map>
#include <numeric>
#include <queue>
#include <set>
#include <sstream>
#include <stack>
#include <string>
#include <unistd.h>
#include <unordered_map>
#include <vector>
using namespace std;
typedef long long ll;
typedef vector<int> vi;
typedef vector<ll> vl;
typedef vector<vl> vvl;
typedef vector<vvl> vvvl;
typedef vector<vi> vvi;
typedef vector<vvi> vvvi;
typedef vector<bool> vb;
typedef vector<vector<bool>> vvb;
typedef vector<string> vs;
typedef vector<vector<string>> vvs;
typedef vector<char> vc;
typedef vector<vector<char>> vvc;
typedef vector<double> vd;
typedef vector<vd> vvd;
typedef vector<vvd> vvvd;
typedef pair<int, int> P;
typedef pair<ll, ll> PL;
typedef vector<P> vp;
typedef vector<PL> vpl;
typedef vector<vector<P>> vvp;
typedef vector<vector<PL>> vvpl;
const int INF = 1001001001;
const ll LINF = 1e12;
const double pi = 3.1415926535897932;
const string endstr = "\n";
#define FOR(i, a, b) for (ll i = (a); i < b; i++)
#define REP(i, n) for (ll i = 0; i < n; i++)
#define FORMAP(it, m) for (auto it = m.begin(); it != m.end(); it++)
#define ff first
#define ss second
#define pb push_back

template <typename T> T gcd(T a, T b) { return (a == 0) ? b : gcd(b % a, a); }
template <typename T> T lcm(T a, T b) { return a / gcd(a, b) * b; }

bool p_comp_fs(const PL p1, const PL p2) { return p1.first < p2.first; };
bool p_comp_fg(const PL p1, const PL p2) { return p1.first > p2.first; };
bool p_comp_ss(const PL p1, const PL p2) { return p1.second < p2.second; };
bool p_comp_sg(const PL p1, const PL p2) { return p1.second > p2.second; };
template <typename T> vector<T> uniquen(vector<T> vec) {
  vec.erase(unique(vec.begin(), vec.end()), vec.end());
  return vec;
}

const ll mod = 1e9 + 7;

int main() {
  ll N, K;
  cin >> N >> K;
  vl a(N);
  REP(i, N) cin >> a[i];

  vvl dp(N + 1, vl(K + 1, 0));
  REP(i, K + 1) if (i <= a[0]) dp[1][i] = 1;
  FOR(i, 1, N) {
    vl sum(K + 2, 0);
    REP(j, K + 1) sum[j + 1] = (sum[j] + dp[i][j]) % mod;
    REP(l, K + 1) {
      dp[i + 1][l] = (sum[l + 1] - sum[max(l - a[i], 0ll)] + mod) % mod;
    }
  }
  cout << dp[N][K] % mod << endl;
  return 0;
}