Problem p01450 (C++)

Buggy submission (status: Runtime Error):
#ifndef LOCAL
#pragma GCC optimize("Ofast")
#endif
#include <algorithm>
#include <bitset>
#include <cassert>
#include <complex>
#include <deque>
#include <functional>
#include <iomanip>
#include <iostream>
#include <list>
#include <map>
#include <queue>
#include <random>
#include <set>
#include <stack>
#include <unordered_map>
#include <unordered_set>

using namespace std;
using i64 = int_fast64_t;
using db = double;
using ldb = long double;
using pii = pair<int, int>;
using pli = pair<int_fast64_t, int>;
using pll = pair<int_fast64_t, int_fast64_t>;
using pdi = pair<double, int>;
using pdd = pair<double, double>;
template <class T> using vct = vector<T>;
template <class T> using heap = priority_queue<T>;
template <class T> using minheap = priority_queue<T, vector<T>, greater<T>>;
template <class T> constexpr T inf = numeric_limits<T>::max() / (T)16;
constexpr int dx[9] = {1, 0, -1, 0, 1, -1, -1, 1, 0};
constexpr int dy[9] = {0, 1, 0, -1, 1, 1, -1, -1, 0};
constexpr long double Pi = 3.1415926535897932384626433832795028;
constexpr long double Golden = 1.61803398874989484820;
constexpr long double eps = 1e-15;

#define iostream_untie true
#define mod 1000000007LL
#define stdout_precision 10
#define stderr_precision 6
#define itrep(i, v) for (auto i = begin(v); i != end(v); ++i)
#define ritrep(i, v) for (auto i = rbegin(v); i != rend(v); ++i)
#define rep(i, n) for (int i = 0; i < (n); ++i)
#define rrep(i, n) for (int i = (n)-1; i >= 0; --i)
#define all(v) begin(v), end(v)
#define rall(v) rbegin(v), rend(v)
#define fir first
#define sec second
#define u_map unordered_map
#define u_set unordered_set
#define l_bnd lower_bound
#define u_bnd upper_bound
#define rsz resize
#define ers erase
#define emp emplace
#define emf emplace_front
#define emb emplace_back
#define pof pop_front
#define pob pop_back
#define mkp make_pair
#define mkt make_tuple
#define popcnt __builtin_popcount

namespace setup {
struct setupper {
  setupper() {
    if (iostream_untie) {
      ios::sync_with_stdio(false);
      std::cin.tie(nullptr);
      std::cout.tie(nullptr);
      std::cerr.tie(nullptr);
    }
    std::cout << std::fixed << std::setprecision(stdout_precision);
    std::cerr << std::fixed << std::setprecision(stderr_precision);
#ifdef LOCAL
    if (!freopen("input.txt", "rt", stdin)) {
      std::cerr << "Failed to open the input file.\n";
      std::exit(EXIT_FAILURE);
    }
    // if(!freopen("output.txt","wt",stdout)) {
    //     cerr << "Failed to open the output file.\n"; exit(EXIT_FAILURE);
    // }
    // std::cerr << "\n---stderr---\n";
    // auto print_atexit = []() {
    //     std::cerr << "Exec time : " << clock() / (double)CLOCKS_PER_SEC *
    //     1000.0 << "ms\n"; std::cerr << "------------\n";
    // };
    // atexit((void(*)())print_atexit);
    // atexit((void(*)())fclose(stdin));
#endif
  }
} __setupper;
} // namespace setup

namespace std {
template <class RAitr> void rsort(RAitr __first, RAitr __last) {
  sort(__first, __last, greater<>());
}
template <class T> void hash_combine(size_t &seed, T const &key) {
  seed ^= hash<T>()(key) + 0x9e3779b9 + (seed << 6) + (seed >> 2);
}
template <class T, class U> struct hash<pair<T, U>> {
  size_t operator()(pair<T, U> const &pr) const {
    size_t seed = 0;
    hash_combine(seed, pr.first);
    hash_combine(seed, pr.second);
    return seed;
  }
};
template <class Tup, size_t index = tuple_size<Tup>::value - 1>
struct hashval_calc {
  static void apply(size_t &seed, Tup const &tup) {
    hashval_calc<Tup, index - 1>::apply(seed, tup);
    hash_combine(seed, get<index>(tup));
  }
};
template <class Tup> struct hashval_calc<Tup, 0> {
  static void apply(size_t &seed, Tup const &tup) {
    hash_combine(seed, get<0>(tup));
  }
};
template <class... T> struct hash<tuple<T...>> {
  size_t operator()(tuple<T...> const &tup) const {
    size_t seed = 0;
    hashval_calc<tuple<T...>>::apply(seed, tup);
    return seed;
  }
};
} // namespace std

template <class T, class U> istream &operator>>(istream &s, pair<T, U> &p) {
  return s >> p.first >> p.second;
}
template <class T, class U>
ostream &operator<<(ostream &s, const pair<T, U> p) {
  return s << p.first << " " << p.second;
}
template <class T> istream &operator>>(istream &s, vector<T> &v) {
  for (T &e : v)
    s >> e;
  return s;
}
template <class T> ostream &operator<<(ostream &s, const vector<T> &v) {
  for (size_t i = 0; i < v.size(); ++i)
    s << (i ? " " : "") << v[i];
  return s;
}
#define dump(...)                                                              \
  cerr << " [ " << __LINE__ << " : " << __FUNCTION__ << " ] " << #__VA_ARGS__  \
       << " : ";                                                               \
  dump_func(__VA_ARGS__)
template <class T> void dump_func(T x) { cerr << x << '\n'; }
template <class T, class... Rest> void dump_func(T x, Rest... rest) {
  cerr << x << ",";
  dump_func(rest...);
}
template <class T = i64> T read() {
  T x;
  return cin >> x, x;
}
template <class T> void write(T x) { cout << x << '\n'; }
template <class T, class... Rest> void write(T x, Rest... rest) {
  cout << x << ' ';
  write(rest...);
}
void writeln() {}
template <class T, class... Rest> void writeln(T x, Rest... rest) {
  cout << x << '\n';
  writeln(rest...);
}
#define esc(...) writeln(__VA_ARGS__), exit(0)

namespace updater {
template <class T> static void add(T &x, const T &y) { x += y; }
template <class T> static void ext_add(T &x, const T &y, size_t w) {
  x += y * w;
}
template <class T> static void mul(T &x, const T &y) { x *= y; }
template <class T> static void ext_mul(T &x, const T &y, size_t w) {
  x *= (T)pow(y, w);
}
template <class T> static bool chmax(T &x, const T &y) {
  return x < y ? x = y, true : false;
}
template <class T> static bool chmin(T &x, const T &y) {
  return x > y ? x = y, true : false;
}
}; // namespace updater
using updater::add;
using updater::chmax;
using updater::chmin;

template <class T> constexpr T minf(const T &x, const T &y) {
  return min(x, y);
}
template <class T> constexpr T maxf(const T &x, const T &y) {
  return max(x, y);
}
constexpr bool bit(i64 n, int e) { return (n >> e) & 1; }
constexpr int_fast64_t mask(int_fast64_t n, int e) {
  return n & ((1 << e) - 1);
}
constexpr int ilog(int_fast64_t x, int_fast64_t b = 2) {
  return x ? 1 + ilog(x / b, b) : -1;
}
template <class F>
int_fast64_t binry(int_fast64_t ok, int_fast64_t ng, const F &fn) {
  while (abs(ok - ng) > 1) {
    int_fast64_t mid = (ok + ng) / 2;
    (fn(mid) ? ok : ng) = mid;
  }
  return ok;
}
template <class A, size_t N, class T> void init(A (&array)[N], const T &val) {
  fill((T *)array, (T *)(array + N), val);
}
template <class T> vector<int> cmprs(const vector<T> &v) {
  vector<T> tmp = v;
  vector<int> ret;
  sort(begin(tmp), end(tmp));
  tmp.erase(unique(begin(tmp), end(tmp)), end(tmp));
  for (T i : v)
    ret.emplace_back(lower_bound(begin(tmp), end(tmp), i) - begin(tmp));
  return ret;
}
template <class T> vector<int> cmprs(const T *__first, const T *__last) {
  return cmprs(vector<T>(__first, __last));
}
template <class F> void for_subset(uint_fast64_t s, const F &fn) {
  uint_fast64_t tmp = s;
  do {
    fn(tmp);
  } while ((--tmp &= s) != s);
}

/* The main code follows. */

struct modint {
  int x;
  constexpr modint() : x(0) {}
  constexpr modint(int_fast64_t y)
      : x(y >= 0 ? y % mod : (mod - (-y) % mod) % mod) {}

  constexpr modint &operator+=(const modint &p) {
    if ((x += p.x) >= mod)
      x -= mod;
    return *this;
  }

  constexpr modint &operator++() { return ++x, *this; }

  constexpr modint operator++(int) {
    modint t = *this;
    return ++x, t;
  }

  constexpr modint &operator-=(const modint &p) {
    if ((x += mod - p.x) >= mod)
      x -= mod;
    return *this;
  }

  constexpr modint &operator--() { return --x, *this; }

  constexpr modint operator--(int) {
    modint t = *this;
    return --x, t;
  }

  constexpr modint &operator*=(const modint &p) {
    x = (int)(1LL * x * p.x % mod);
    return *this;
  }

  constexpr modint &operator/=(const modint &p) {
    *this *= inverse(p);
    return *this;
  }

  constexpr modint operator-() { return modint(-x); }

  constexpr modint operator+(const modint &p) { return modint(*this) += p; }

  constexpr modint operator-(const modint &p) { return modint(*this) -= p; }

  constexpr modint operator*(const modint &p) { return modint(*this) *= p; }

  constexpr modint operator/(const modint &p) { return modint(*this) /= p; }

  constexpr bool operator==(const modint &p) { return x == p.x; }

  constexpr bool operator!=(const modint &p) { return x != p.x; }

  constexpr bool operator!() { return !x; }

  constexpr bool operator>(const modint &p) { return x > p.x; }

  constexpr bool operator<(const modint &p) { return x < p.x; }

  constexpr bool operator>=(const modint &p) { return x >= p.x; }

  constexpr bool operator<=(const modint &p) { return x <= p.x; }

  constexpr static modint inverse(const modint &p) {
    int a = p.x, b = mod, u = 1, v = 0;
    while (b > 0) {
      int t = a / b;
      a -= t * b;
      a ^= b ^= a ^= b;
      u -= t * v;
      u ^= v ^= u ^= v;
    }
    return modint(u);
  }

  constexpr static modint pow(modint p, uint_fast64_t e) {
    if (!e)
      return 1;
    return pow(p * p, e >> 1) * (e & 1 ? p : 1);
  }

  friend ostream &operator<<(ostream &s, const modint &p) { return s << p.x; }

  friend istream &operator>>(istream &s, modint &p) {
    uint_fast64_t x;
    p = modint((s >> x, x));
    return s;
  }
};

int n, W;
int w[210];
int s[210];
modint dp[10101], ans;

signed main() {
  cin >> n >> W;
  rep(i, n) { cin >> w[i]; }
  sort(w, w + n);
  for (int i = 0; i < n; ++i) {
    s[i + 1] = s[i] + w[i];
  }
  dp[W] = 1;
  if (W >= s[n])
    ans++;
  for (int i = n - 1; i >= 0; --i) {
    for (int x = s[i]; x - s[i] < w[i]; ++x) {
      ans += dp[x];
    }
    for (int x = 0; x + w[i] <= W; ++x) {
      dp[x] += dp[x + w[i]];
    }
  }
  esc(ans);
}


Fixed submission:
#ifndef LOCAL
#pragma GCC optimize("Ofast")
#endif
#include <algorithm>
#include <bitset>
#include <cassert>
#include <complex>
#include <deque>
#include <functional>
#include <iomanip>
#include <iostream>
#include <list>
#include <map>
#include <queue>
#include <random>
#include <set>
#include <stack>
#include <unordered_map>
#include <unordered_set>

using namespace std;
using i64 = int_fast64_t;
using db = double;
using ldb = long double;
using pii = pair<int, int>;
using pli = pair<int_fast64_t, int>;
using pll = pair<int_fast64_t, int_fast64_t>;
using pdi = pair<double, int>;
using pdd = pair<double, double>;
template <class T> using vct = vector<T>;
template <class T> using heap = priority_queue<T>;
template <class T> using minheap = priority_queue<T, vector<T>, greater<T>>;
template <class T> constexpr T inf = numeric_limits<T>::max() / (T)16;
constexpr int dx[9] = {1, 0, -1, 0, 1, -1, -1, 1, 0};
constexpr int dy[9] = {0, 1, 0, -1, 1, 1, -1, -1, 0};
constexpr long double Pi = 3.1415926535897932384626433832795028;
constexpr long double Golden = 1.61803398874989484820;
constexpr long double eps = 1e-15;

#define iostream_untie true
#define mod 1000000007LL
#define stdout_precision 10
#define stderr_precision 6
#define itrep(i, v) for (auto i = begin(v); i != end(v); ++i)
#define ritrep(i, v) for (auto i = rbegin(v); i != rend(v); ++i)
#define rep(i, n) for (int i = 0; i < (n); ++i)
#define rrep(i, n) for (int i = (n)-1; i >= 0; --i)
#define all(v) begin(v), end(v)
#define rall(v) rbegin(v), rend(v)
#define fir first
#define sec second
#define u_map unordered_map
#define u_set unordered_set
#define l_bnd lower_bound
#define u_bnd upper_bound
#define rsz resize
#define ers erase
#define emp emplace
#define emf emplace_front
#define emb emplace_back
#define pof pop_front
#define pob pop_back
#define mkp make_pair
#define mkt make_tuple
#define popcnt __builtin_popcount

namespace setup {
struct setupper {
  setupper() {
    if (iostream_untie) {
      ios::sync_with_stdio(false);
      std::cin.tie(nullptr);
      std::cout.tie(nullptr);
      std::cerr.tie(nullptr);
    }
    std::cout << std::fixed << std::setprecision(stdout_precision);
    std::cerr << std::fixed << std::setprecision(stderr_precision);
#ifdef LOCAL
    if (!freopen("input.txt", "rt", stdin)) {
      std::cerr << "Failed to open the input file.\n";
      std::exit(EXIT_FAILURE);
    }
    // if(!freopen("output.txt","wt",stdout)) {
    //     cerr << "Failed to open the output file.\n"; exit(EXIT_FAILURE);
    // }
    // std::cerr << "\n---stderr---\n";
    // auto print_atexit = []() {
    //     std::cerr << "Exec time : " << clock() / (double)CLOCKS_PER_SEC *
    //     1000.0 << "ms\n"; std::cerr << "------------\n";
    // };
    // atexit((void(*)())print_atexit);
    // atexit((void(*)())fclose(stdin));
#endif
  }
} __setupper;
} // namespace setup

namespace std {
template <class RAitr> void rsort(RAitr __first, RAitr __last) {
  sort(__first, __last, greater<>());
}
template <class T> void hash_combine(size_t &seed, T const &key) {
  seed ^= hash<T>()(key) + 0x9e3779b9 + (seed << 6) + (seed >> 2);
}
template <class T, class U> struct hash<pair<T, U>> {
  size_t operator()(pair<T, U> const &pr) const {
    size_t seed = 0;
    hash_combine(seed, pr.first);
    hash_combine(seed, pr.second);
    return seed;
  }
};
template <class Tup, size_t index = tuple_size<Tup>::value - 1>
struct hashval_calc {
  static void apply(size_t &seed, Tup const &tup) {
    hashval_calc<Tup, index - 1>::apply(seed, tup);
    hash_combine(seed, get<index>(tup));
  }
};
template <class Tup> struct hashval_calc<Tup, 0> {
  static void apply(size_t &seed, Tup const &tup) {
    hash_combine(seed, get<0>(tup));
  }
};
template <class... T> struct hash<tuple<T...>> {
  size_t operator()(tuple<T...> const &tup) const {
    size_t seed = 0;
    hashval_calc<tuple<T...>>::apply(seed, tup);
    return seed;
  }
};
} // namespace std

template <class T, class U> istream &operator>>(istream &s, pair<T, U> &p) {
  return s >> p.first >> p.second;
}
template <class T, class U>
ostream &operator<<(ostream &s, const pair<T, U> p) {
  return s << p.first << " " << p.second;
}
template <class T> istream &operator>>(istream &s, vector<T> &v) {
  for (T &e : v)
    s >> e;
  return s;
}
template <class T> ostream &operator<<(ostream &s, const vector<T> &v) {
  for (size_t i = 0; i < v.size(); ++i)
    s << (i ? " " : "") << v[i];
  return s;
}
#define dump(...)                                                              \
  cerr << " [ " << __LINE__ << " : " << __FUNCTION__ << " ] " << #__VA_ARGS__  \
       << " : ";                                                               \
  dump_func(__VA_ARGS__)
template <class T> void dump_func(T x) { cerr << x << '\n'; }
template <class T, class... Rest> void dump_func(T x, Rest... rest) {
  cerr << x << ",";
  dump_func(rest...);
}
template <class T = i64> T read() {
  T x;
  return cin >> x, x;
}
template <class T> void write(T x) { cout << x << '\n'; }
template <class T, class... Rest> void write(T x, Rest... rest) {
  cout << x << ' ';
  write(rest...);
}
void writeln() {}
template <class T, class... Rest> void writeln(T x, Rest... rest) {
  cout << x << '\n';
  writeln(rest...);
}
#define esc(...) writeln(__VA_ARGS__), exit(0)

namespace updater {
template <class T> static void add(T &x, const T &y) { x += y; }
template <class T> static void ext_add(T &x, const T &y, size_t w) {
  x += y * w;
}
template <class T> static void mul(T &x, const T &y) { x *= y; }
template <class T> static void ext_mul(T &x, const T &y, size_t w) {
  x *= (T)pow(y, w);
}
template <class T> static bool chmax(T &x, const T &y) {
  return x < y ? x = y, true : false;
}
template <class T> static bool chmin(T &x, const T &y) {
  return x > y ? x = y, true : false;
}
}; // namespace updater
using updater::add;
using updater::chmax;
using updater::chmin;

template <class T> constexpr T minf(const T &x, const T &y) {
  return min(x, y);
}
template <class T> constexpr T maxf(const T &x, const T &y) {
  return max(x, y);
}
constexpr bool bit(i64 n, int e) { return (n >> e) & 1; }
constexpr int_fast64_t mask(int_fast64_t n, int e) {
  return n & ((1 << e) - 1);
}
constexpr int ilog(int_fast64_t x, int_fast64_t b = 2) {
  return x ? 1 + ilog(x / b, b) : -1;
}
template <class F>
int_fast64_t binry(int_fast64_t ok, int_fast64_t ng, const F &fn) {
  while (abs(ok - ng) > 1) {
    int_fast64_t mid = (ok + ng) / 2;
    (fn(mid) ? ok : ng) = mid;
  }
  return ok;
}
template <class A, size_t N, class T> void init(A (&array)[N], const T &val) {
  fill((T *)array, (T *)(array + N), val);
}
template <class T> vector<int> cmprs(const vector<T> &v) {
  vector<T> tmp = v;
  vector<int> ret;
  sort(begin(tmp), end(tmp));
  tmp.erase(unique(begin(tmp), end(tmp)), end(tmp));
  for (T i : v)
    ret.emplace_back(lower_bound(begin(tmp), end(tmp), i) - begin(tmp));
  return ret;
}
template <class T> vector<int> cmprs(const T *__first, const T *__last) {
  return cmprs(vector<T>(__first, __last));
}
template <class F> void for_subset(uint_fast64_t s, const F &fn) {
  uint_fast64_t tmp = s;
  do {
    fn(tmp);
  } while ((--tmp &= s) != s);
}

/* The main code follows. */

struct modint {
  int x;
  constexpr modint() : x(0) {}
  constexpr modint(int_fast64_t y)
      : x(y >= 0 ? y % mod : (mod - (-y) % mod) % mod) {}

  constexpr modint &operator+=(const modint &p) {
    if ((x += p.x) >= mod)
      x -= mod;
    return *this;
  }

  constexpr modint &operator++() { return ++x, *this; }

  constexpr modint operator++(int) {
    modint t = *this;
    return ++x, t;
  }

  constexpr modint &operator-=(const modint &p) {
    if ((x += mod - p.x) >= mod)
      x -= mod;
    return *this;
  }

  constexpr modint &operator--() { return --x, *this; }

  constexpr modint operator--(int) {
    modint t = *this;
    return --x, t;
  }

  constexpr modint &operator*=(const modint &p) {
    x = (int)(1LL * x * p.x % mod);
    return *this;
  }

  constexpr modint &operator/=(const modint &p) {
    *this *= inverse(p);
    return *this;
  }

  constexpr modint operator-() { return modint(-x); }

  constexpr modint operator+(const modint &p) { return modint(*this) += p; }

  constexpr modint operator-(const modint &p) { return modint(*this) -= p; }

  constexpr modint operator*(const modint &p) { return modint(*this) *= p; }

  constexpr modint operator/(const modint &p) { return modint(*this) /= p; }

  constexpr bool operator==(const modint &p) { return x == p.x; }

  constexpr bool operator!=(const modint &p) { return x != p.x; }

  constexpr bool operator!() { return !x; }

  constexpr bool operator>(const modint &p) { return x > p.x; }

  constexpr bool operator<(const modint &p) { return x < p.x; }

  constexpr bool operator>=(const modint &p) { return x >= p.x; }

  constexpr bool operator<=(const modint &p) { return x <= p.x; }

  constexpr static modint inverse(const modint &p) {
    int a = p.x, b = mod, u = 1, v = 0;
    while (b > 0) {
      int t = a / b;
      a -= t * b;
      a ^= b ^= a ^= b;
      u -= t * v;
      u ^= v ^= u ^= v;
    }
    return modint(u);
  }

  constexpr static modint pow(modint p, uint_fast64_t e) {
    if (!e)
      return 1;
    return pow(p * p, e >> 1) * (e & 1 ? p : 1);
  }

  friend ostream &operator<<(ostream &s, const modint &p) { return s << p.x; }

  friend istream &operator>>(istream &s, modint &p) {
    uint_fast64_t x;
    p = modint((s >> x, x));
    return s;
  }
};

int n, W;
int w[210];
int s[210];
modint dp[10101], ans;

signed main() {
  cin >> n >> W;
  rep(i, n) { cin >> w[i]; }
  sort(w, w + n);
  for (int i = 0; i < n; ++i) {
    s[i + 1] = s[i] + w[i];
  }
  dp[W] = 1;
  if (W >= s[n])
    ans++;
  for (int i = n - 1; i >= 0; --i) {
    for (int x = s[i]; x <= W && x - s[i] < w[i]; ++x) {
      ans += dp[x];
    }
    for (int x = 0; x + w[i] <= W; ++x) {
      dp[x] += dp[x + w[i]];
    }
  }
  esc(ans);
}