ABC - version two

#include <bits/stdc++.h>

using namespace std;

ifstream fin("adece.in");
ofstream fout("adece.out");

const int mod = 1e8 + 7;
const int kN = 9e3;
int f[1 + kN], invf[1 + kN];

void addSelf(int &x, const int &y) {
  x += y;
  if (x >= mod) {
    x -= mod;
  }
}

int add(int x, const int &y) {
  addSelf(x, y);
  return x;
}

void multSelf(int &x, const int &y) {
  x = (int64_t)x * y % mod;
}

int mult(int x, const int &y) {
  multSelf(x, y);
  return x;
}

int Pow(int x, int n) {
  int ans = 1;

  while (n) {
    if (n & 1) {
      multSelf(ans, x);
    }
    multSelf(x, x);
    n >>= 1;
  }

  return ans;
}

int invers(int x) {
  return Pow(x, mod - 2);
}

void computeFactorials(int n) {
  f[0] = f[1] = 1;
  for (int i = 2; i <= n; ++i) {
    f[i] = mult(f[i - 1], i);
  }

  invf[n] = invers(f[n]);
  for (int i = n - 1; i >= 0; --i) {
    invf[i] = mult(invf[i + 1], i + 1);
  }
}

int main() {
  int a, b, c;
  fin >> a >> b >> c;

  int n = a + b + c, m = min({a, b, c});

  computeFactorials(n);

  int res = 0;

  for (int i = 0; i <= m; ++i) {
    int remA = a - i;
    int remB = b - i;
    int remC = c - i;
    int remN = remA + remB + remC + i;

    int ways = mult(f[remN], mult(mult(invf[remA], invf[remB]), mult(invf[remC], invf[i])));

    if (i % 2 == 0) {
      addSelf(res, ways);
    } else {
      addSelf(res, mod - ways);
    }
  }

  fout << res  << '\n';

  fin.close();
  fout.close();

  return 0;
}