Language: C++

/*
 * atcoder/dp/m.cpp
 */

// C++ 14
#include <iostream>
#include <string>
#include <vector>
#include <list>
#include <algorithm>
#include <queue>
#include <stack>
#include <set>
#include <map>
#include <unordered_map>
#include <cstring>

#define ll long long
#define Int ll
#define loop(__x, __start, __end) for(Int __x = __start; __x < __end; __x++)
#define loopdown(__x, __start, __end) for(Int __x = __start; __x > __end; __x--)
#define rep(__n) for(Int __x = 0; __x < __n; __x++)
#define span(__a,__x,__y) __a.begin()+__x,__a.begin()+__y
#define span_all(__a) __a.begin(),__a.end()
#define len(__x) (__x.size())
#define last(__x) (__x[__x.size()-1])

using namespace std;

#define MOD 1000000007

template <class T> bool chmin(T &a, T b) { if (a > b) {a = b; return true; } return false; }
template <class T> bool chmax(T &a, T b) { if (a < b) {a = b; return true; } return false; }


struct Point {
  Int x, y;
  Point(Int x, Int y): x(x), y(y) {}
  Point(): x(0), y(0) {}

  Point operator + (Point v) { return Point(x + v.x, y + v.y); }
  Point operator - (Point v) { return Point(x - v.x, y - v.y); }
  bool operator == (const Point &v) const {
    return x == v.x && y == v.y;
  }
  bool operator< (const Point &p1) const {
    return x < p1.x && y < p1.y;
  }
};
ostream & operator << (ostream & out, Point const & v) {
  out << "Point(" << v.x << ", " << v.y << ')';
  return out;
}

istream & operator >> (istream & in, Point & v) {
  Int x, y;
  in >> x; in >> y; v.x = x; v.y = y;
  return in;
}

// Geometry

#define EPS 0.0000000001

class Vector2 {
public:
  double x, y;
  
  Vector2(double x = 0, double y = 0): x(x), y(y) {}
  
  Vector2 operator + (Vector2 v) { return Vector2(x + v.x, y + v.y); }
  Vector2 operator - (Vector2 v) { return Vector2(x - v.x, y - v.y); }
  Vector2 operator * (double k) { return Vector2(x * k, y * k); }
  Vector2 operator / (double k) { return Vector2(x / k, y / k); }
  
  double length() { return sqrt(norm()); }
  double norm() { return x * x + y * y; }
  double dot (Vector2 v) { return x * v.x + y * v.y; }
  double cross (Vector2 v) { return x * v.y - y * v.x; }
  
  bool operator < (const Vector2 &v) const {
    return x != v.x ? x < v.x : y < v.y;
  }
  
  bool operator == (const Vector2 &v) const {
    return fabs(x - v.x) < EPS && fabs(y - v.y) < EPS;
  }
};

ostream & operator << (ostream & out, Vector2 const & v) { 
  out<< "Vector2(" << v.x << ", " << v.y << ')';
  return out;
}

istream & operator >> (istream & in, Vector2 & v) { 
  double x, y;
  in >> x;
  in >> y;
  v.x = x;
  v.y = y;
  return in;
}


vector<Int> slice(vector<Int> &vec, int s, int t) {
  return vector<Int>(vec.begin()+s, vec.begin()+t);
}

vector<Int> trim(vector<Int> &vec, int n) {
  auto init = slice(vec, 0, n);
  auto tail = slice(vec, n+2, vec.size());
  init.insert(init.end(), tail.begin(), tail.end());
  return init;
}


Int N, K;
vector<Int> A;

void input() {
  cin >> N >> K;
  Int a;
  loop(n,0,N) {
    cin >> a;
    A.push_back(a);
  }
}

Int dp[110][100100];

// 100 * 100000 * 100000 = O(10**12)
Int rec(Int n, Int k) {
  Int &cache = dp[n][k];
  if (~cache) return cache;
  if (k == 0) return cache = 1;
  if (n == N) return cache = 0;

  Int ways = 0;
  Int max_ = min(k, A[n]);
  loop(take, 0, max_+1) {
    ways += rec(n+1, k-take);
    ways %= MOD;
  }

  return cache = ways;
}

Int memoRec() {
  loop(n,0,N+1) loop(k,0,K+1) dp[n][k] = -1;
  return rec(0, K);
}

Int acc[100100];

Int receive() {
  memset(dp, 0, sizeof(dp));
  dp[0][0] = 1;
  loop(n,1,N+1) {
    loop(k,0,K+1) {
      acc[k+1] = (acc[k] + dp[n-1][k]) % MOD;
    }

    loop(k,0,K+1) {
      dp[n][k] = (acc[k+1] - acc[max(0LL, k-A[n-1])] + MOD) % MOD;
    }
  }

  return dp[N][K];
}

void dump() {
  loop(k,0,K+1) {
    loop(n,0,N+1) {
      cout << dp[n][k] << " ";
    }
    cout << endl;
  }
}

void solve() {
  // Int r = memoRec();
  Int r = receive();
  cout << r << endl;
  // dump();
}

int main() {
  // cout.precision(15);
  input();
  solve();
  return 0;
}


Compiler output:
a.cc: In member function 'double Vector2::length()':
a.cc:76:28: error: 'sqrt' was not declared in this scope
   76 |   double length() { return sqrt(norm()); }
      |                            ^~~~
a.cc: In member function 'bool Vector2::operator==(const Vector2&) const':
a.cc:86:12: error: 'fabs' was not declared in this scope; did you mean 'labs'?
   86 |     return fabs(x - v.x) < EPS && fabs(y - v.y) < EPS;
      |            ^~~~
      |            labs