Problem p01939 (C++) — buggy submission, verdict: Runtime Error

#include <bits/stdc++.h>
using namespace std;
/*{{{*/ // template
#define rep(i, n) for (int i = 0; i < n; i++)
constexpr int INF = numeric_limits<int>::max() / 2;
constexpr long long LINF = numeric_limits<long long>::max() / 3;
#define mp make_pair
#define pb push_back
#define eb emplace_back
#define fi first
#define se second
#define all(v) (v).begin(), (v).end()
#define sz(x) (int)(x).size()
#define debug(x) cerr << #x << ":" << x << endl
#define debug2(x, y) cerr << #x << "," << #y ":" << x << "," << y << endl
// struct fin{ fin(){ cin.tie(0); ios::sync_with_stdio(false); } } fin_;
struct Double {
  double d;
  explicit Double(double x) : d(x) {}
};
ostream &operator<<(ostream &os, const Double x) {
  os << fixed << setprecision(20) << x.d;
  return os;
}
template <typename T> ostream &operator<<(ostream &os, const vector<T> &vec) {
  os << "[";
  for (const auto &v : vec) {
    os << v << ",";
  }
  os << "]";
  return os;
}
template <typename T, typename U>
ostream &operator<<(ostream &os, const pair<T, U> &p) {
  os << "(" << p.first << "," << p.second << ")";
  return os;
}
template <typename T> ostream &operator<<(ostream &os, const set<T> &st) {
  os << "{";
  for (T v : st)
    os << v << ",";
  os << "}";
  return os;
}
template <typename T, typename U> inline void chmax(T &x, U y) {
  if (y > x)
    x = y;
}
template <typename T, typename U> inline void chmin(T &x, U y) {
  if (y < x)
    x = y;
}
typedef long long ll;
typedef unsigned long long ull;
typedef pair<int, int> pii;
typedef vector<int> vi;
typedef vector<vi> vvi;
ll gcd(ll a, ll b) {
  if (b == 0)
    return a;
  else
    return gcd(b, a % b);
}
// constexpr double eps = 1e-14;
constexpr double eps = 1e-10;
constexpr ll mod = 1e9 + 7;
const int dx[] = {1, 0, -1, 0}, dy[] = {0, 1, 0, -1};
/*}}}*/

ll n, m;

int main() {
  cin >> n >> m;

  if (n == 1) {
    cout << (m + 1) % mod << endl;
    return 0;
  }

  /*
   * n?????????????´??????? s[n-1] = s[0] + d * (n-1)
   * d??????
   * 0 <= s[0] + d * (n-1) <= m
   *
   * d = 0 --> m + 1 ??????
   *
   * d > 0 (d < 0 ???????????????????§°???)
   *  --> d?????¶?´? : 0 < d <= m/(n-1) (=ub??¨??????)
   *  --> d??????????????????????????¨????????¨
   *  --> 0 <= s[0] <= m-d(n-1) :: m+1-d(n-1) ??????
   *  --> ?£m+1-d(n-1) (0 < d <= ub)
   *        = (m+1)*ub - (n-1)*(ub*(ub+1))/2 (= a??¨??????)
   *
   *  ????????? m + 1 + 2 * a ????????????????
   */

  ll ub = m / (n - 1);
  ll ubmod = ub % mod;

  ll a1 = ((m + 1) % mod) * (ub % mod) % mod; // (m+1)*ub

  ll t1 = (n - 1) % mod;                   // (n-1)
  ll t2 = (ubmod * (ubmod + 1)) / 2 % mod; // (ub*(ub+1))/2
  ll a2 = (t1 * t2) % mod;
  ll a = (a1 - a2 + mod) % mod;
  assert(a >= 0);

  ll b = (m + 1) % mod;

  ll ans = (2 * a % mod + b) % mod;
  cout << ans << endl;
}

Error: 0
a:40
b:10


Fixed submission:

#include <bits/stdc++.h>
using namespace std;
/*{{{*/ // template
#define rep(i, n) for (int i = 0; i < n; i++)
constexpr int INF = numeric_limits<int>::max() / 2;
constexpr long long LINF = numeric_limits<long long>::max() / 3;
#define mp make_pair
#define pb push_back
#define eb emplace_back
#define fi first
#define se second
#define all(v) (v).begin(), (v).end()
#define sz(x) (int)(x).size()
#define debug(x) cerr << #x << ":" << x << endl
#define debug2(x, y) cerr << #x << "," << #y ":" << x << "," << y << endl
// struct fin{ fin(){ cin.tie(0); ios::sync_with_stdio(false); } } fin_;
struct Double {
  double d;
  explicit Double(double x) : d(x) {}
};
ostream &operator<<(ostream &os, const Double x) {
  os << fixed << setprecision(20) << x.d;
  return os;
}
template <typename T> ostream &operator<<(ostream &os, const vector<T> &vec) {
  os << "[";
  for (const auto &v : vec) {
    os << v << ",";
  }
  os << "]";
  return os;
}
template <typename T, typename U>
ostream &operator<<(ostream &os, const pair<T, U> &p) {
  os << "(" << p.first << "," << p.second << ")";
  return os;
}
template <typename T> ostream &operator<<(ostream &os, const set<T> &st) {
  os << "{";
  for (T v : st)
    os << v << ",";
  os << "}";
  return os;
}
template <typename T, typename U> inline void chmax(T &x, U y) {
  if (y > x)
    x = y;
}
template <typename T, typename U> inline void chmin(T &x, U y) {
  if (y < x)
    x = y;
}
typedef long long ll;
typedef unsigned long long ull;
typedef pair<int, int> pii;
typedef vector<int> vi;
typedef vector<vi> vvi;
ll gcd(ll a, ll b) {
  if (b == 0)
    return a;
  else
    return gcd(b, a % b);
}
// constexpr double eps = 1e-14;
constexpr double eps = 1e-10;
constexpr ll mod = 1e9 + 7;
const int dx[] = {1, 0, -1, 0}, dy[] = {0, 1, 0, -1};
/*}}}*/

ll n, m;

int main() {
  cin >> n >> m;

  if (n == 1) {
    cout << m + 1 << endl;
    return 0;
  }

  /*
   * n?????????????´??????? s[n-1] = s[0] + d * (n-1)
   * d??????
   * 0 <= s[0] + d * (n-1) <= m
   * max(0,-d*(n-1)) <= s[0] <= min(m - d*(n-1),m)
   * d >= 0?????´??? 0 <= s[0] <= m-d*(n-1)  --- 1
   * d < 0?????´???  -d*(n-1) <= s[0] <= m   --- 2
   *
   * 1.
   *      0 <= m-d*(n-1)??????d<=m/(n-1)
   *      (m-d*(n-1)+1) for d in {0...m/(n-1)}
   * 2.
   *      -d*(n-1) <= m ??????d>=-m/(n-1)
   *      (m+d*(n-1)+1) for d in {-m/(n-1)...-1}
   *
   * 1?????£.
   *      0 <= m-d*(n-1)??????d<=m/(n-1)
   *      -d*n_ for d in [0,1...ub]
   *      0 + -n_ + -2n_ + -3n_ + ... + -ub*n_
   *
   * 2?????£.
   *      -d*(n-1) <= m ??????d>=-m/(n-1)
   *      d*n_ for d in [lb...-1]
   *
   */

  ll ans = 0;

  ll ub = m / (n - 1);
  ll lb = -ub;

  ll ubmod = ub % mod;

  ll a, b, c;

  a = (m + 1) % mod * ubmod % mod * 2 % mod -
      (n - 1) % mod * ubmod % mod * ((ub + 1) % mod) % mod;
  ans += mod;
  a %= mod;
  debug(a);

  b = (m % mod + 1) % mod;
  debug(b);

  ans = a + b;
  ans %= mod;
  cout << ans << endl;
}