Problem p03039 (C++)

Buggy submission (status: Time Limit Exceeded):
#include <bits/stdc++.h>
#define rep(i, m) for (long long i = 0; i < m; i++)
#define per(i, m) for (long long i = m - 1; i >= 0; i--)
#define FOR(i, n, m) for (long long i = n; i < m; i++)
#define ROF(i, n, m) for (long long i = m - 1; i >= n; i--)
#define SORT(v, n)                                                             \
  do {                                                                         \
    sort(v, v + n);                                                            \
    reverse(v, v + n);                                                         \
  } while (0)
#define all(x) (x).begin(), (x).end()
#define EPS (1e-7)
#define INF (1e18)
#define PI (acos(-1))
#define dump(x) cerr << #x << " = " << (x) << endl;
#define debug(x)                                                               \
  cerr << #x << " = " << (x) << " (L" << __LINE__ << ")"                       \
       << " " << __FILE__ << endl;
using namespace std;
typedef long long ll;
const ll MOD = 1000000007;
typedef pair<ll, ll> LP;

ll POW(ll x, ll n) {
  if (n == 0)
    return 1;
  if (n % 2 == 0)
    return POW(x * x, n / 2) % MOD;
  return x % MOD * POW(x, n - 1) % MOD;
}

ll POW2(ll x, ll n) {
  if (n == 0)
    return 1;
  if (n % 2 == 0)
    return POW2(x * x, n / 2);
  return x * POW2(x, n - 1);
}

ll gcd(ll u, ll v) {
  ll r;
  while (0 != v) {
    r = u % v;
    u = v;
    v = r;
  }
  return u;
}

ll lcm(ll u, ll v) { return u * v / gcd(u, v); }

ll KAI(ll m) {
  if (m < 0)
    return 0;
  if (m == 0)
    return 1;
  return m * KAI(m - 1) % MOD;
}

ll KAI2(ll m) {
  if (m < 0)
    return 0;
  if (m == 0)
    return 1;
  return m * KAI2(m - 1);
}

ll extGCD(ll a, ll b, ll &x, ll &y) {
  if (b == 0) {
    x = 1;
    y = 0;
    return a;
  }
  ll d = extGCD(b, a % b, y, x);
  y -= a / b * x;
  return d;
}

inline ll mod(ll a, ll m) { return (a % m + m) % m; }

ll modinv(ll a) {
  ll x, y;
  extGCD(a, MOD, x, y);
  return mod(x, MOD);
}

ll COM(ll m, ll n) {
  if (m < n)
    return 0;
  if (n < 0)
    return 0;
  if (n == 0)
    return 1;
  if (m == n)
    return 1;
  return KAI(m) % MOD * modinv(KAI(n) % MOD * KAI(m - n) % MOD) % MOD;
}

ll COM2(ll m, ll n) {
  if (m < n)
    return 0;
  if (n < 0)
    return 0;
  if (n == 0)
    return 1;
  if (m == n)
    return 1;
  return KAI2(m) / KAI2(n) / KAI2(m - n);
}

ll DEC(ll x, ll m, ll n) { return x % POW(m, n + 1) / POW(m, n); }

ll keta(ll x, ll n) {
  if (x == 0)
    return 0;
  return keta(x / n, n) + 1;
}

ll DIV(ll x, ll n) {
  if (x == 0)
    return 0;
  return x / n + DIV(x / n, n);
}

ll ORD(ll x, ll n) {
  if (x == 0)
    return INF;
  if (x % n != 0)
    return 0;
  return 1 + ORD(x / n, n);
}

int main() {
  ll n, m, k, ans, q = 0;
  cin >> n >> m >> k;
  rep(i, n) { q = (q + (COM(i + 1, 2) + COM(n - i, 2)) * m % MOD * m) % MOD; }
  rep(j, m) { q = (q + (COM(j + 1, 2) + COM(m - j, 2)) * n % MOD * n) % MOD; }
  q = q * modinv(COM(m * n, 2)) % MOD * modinv(2) % MOD;
  ans = (COM(n * m, k) * COM(k, 2) % MOD * q % MOD + MOD) % MOD;
  printf("%lld", ans);
}

Fixed submission:
#include <bits/stdc++.h>
#define rep(i, m) for (long long i = 0; i < m; i++)
#define per(i, m) for (long long i = m - 1; i >= 0; i--)
#define FOR(i, n, m) for (long long i = n; i < m; i++)
#define ROF(i, n, m) for (long long i = m - 1; i >= n; i--)
#define SORT(v, n)                                                             \
  do {                                                                         \
    sort(v, v + n);                                                            \
    reverse(v, v + n);                                                         \
  } while (0)
#define all(x) (x).begin(), (x).end()
#define EPS (1e-7)
#define INF (1e18)
#define PI (acos(-1))
#define dump(x) cerr << #x << " = " << (x) << endl;
#define debug(x)                                                               \
  cerr << #x << " = " << (x) << " (L" << __LINE__ << ")"                       \
       << " " << __FILE__ << endl;
using namespace std;
typedef long long ll;
const ll MOD = 1000000007;
typedef pair<ll, ll> LP;

ll POW(ll x, ll n) {
  if (n == 0)
    return 1;
  if (n % 2 == 0)
    return POW(x * x, n / 2) % MOD;
  return x % MOD * POW(x, n - 1) % MOD;
}

ll POW2(ll x, ll n) {
  if (n == 0)
    return 1;
  if (n % 2 == 0)
    return POW2(x * x, n / 2);
  return x * POW2(x, n - 1);
}

ll gcd(ll u, ll v) {
  ll r;
  while (0 != v) {
    r = u % v;
    u = v;
    v = r;
  }
  return u;
}

ll lcm(ll u, ll v) { return u * v / gcd(u, v); }

ll KAI(ll m) {
  if (m < 0)
    return 0;
  if (m == 0)
    return 1;
  return m * KAI(m - 1) % MOD;
}

ll KAI2(ll m) {
  if (m < 0)
    return 0;
  if (m == 0)
    return 1;
  return m * KAI2(m - 1);
}

ll extGCD(ll a, ll b, ll &x, ll &y) {
  if (b == 0) {
    x = 1;
    y = 0;
    return a;
  }
  ll d = extGCD(b, a % b, y, x);
  y -= a / b * x;
  return d;
}

inline ll mod(ll a, ll m) { return (a % m + m) % m; }

ll modinv(ll a) {
  ll x, y;
  extGCD(a, MOD, x, y);
  return mod(x, MOD);
}

ll COM(ll m, ll n) {
  if (m < n)
    return 0;
  if (n < 0)
    return 0;
  if (n == 0)
    return 1;
  if (m == n)
    return 1;
  return KAI(m) % MOD * modinv(KAI(n) % MOD * KAI(m - n) % MOD) % MOD;
}

ll COM2(ll m, ll n) {
  if (m < n)
    return 0;
  if (n < 0)
    return 0;
  if (n == 0)
    return 1;
  if (m == n)
    return 1;
  return KAI2(m) / KAI2(n) / KAI2(m - n);
}

ll DEC(ll x, ll m, ll n) { return x % POW(m, n + 1) / POW(m, n); }

ll keta(ll x, ll n) {
  if (x == 0)
    return 0;
  return keta(x / n, n) + 1;
}

ll DIV(ll x, ll n) {
  if (x == 0)
    return 0;
  return x / n + DIV(x / n, n);
}

ll ORD(ll x, ll n) {
  if (x == 0)
    return INF;
  if (x % n != 0)
    return 0;
  return 1 + ORD(x / n, n);
}

int main() {
  ll n, m, k, ans, q = 0;
  cin >> n >> m >> k;
  q = (q + (COM(n + 1, 3) + COM(n + 1, 3)) * m % MOD * m) % MOD;
  q = (q + (COM(m + 1, 3) + COM(m + 1, 3)) * n % MOD * n) % MOD;
  q = q * modinv(COM(m * n, 2)) % MOD * modinv(2) % MOD;
  ans = (COM(n * m, k) * COM(k, 2) % MOD * q % MOD + MOD) % MOD;
  printf("%lld", ans);
}