Language: C++

#include <iostream>
#include <vector>
#include <queue>
#include <math.h>
#include <set>
#define FOR(i, n, m) for(ll i = n; i < (int)m; i++)
#define REP(i, n) FOR(i, 0, n)
#define ALL(v) v.begin(), v.end()
#define pb push_back
using namespace std;
using ll = std::int_fast64_t;
using P = pair<ll, ll>;
constexpr ll inf = 1000000000;
constexpr ll mod = 1000000007;
constexpr long double eps = 1e-15;
template<typename T1, typename T2>
ostream& operator<<(ostream& os, pair<T1, T2> p) {
    os << to_string(p.first) << " " << to_string(p.second);
    return os;
}
template<typename T>
ostream& operator<<(ostream& os, vector<T>& v) {
    REP(i, v.size()) {
        if(i) os << " ";
        os << to_string(v[i]);
    }
    return os;
}

struct modint {
    ll n;
public:
    modint(const ll n = 0) : n((n % mod + mod) % mod) {}
    static modint pow(modint a, int m) {
        modint r = 1;
        while(m > 0) {
            if(m & 1) { r *= a; }
            a = (a * a); m /= 2;
        }
        return r;
    }
    modint &operator++() { *this += 1; return *this; }
    modint &operator--() { *this -= 1; return *this; }
    modint operator++(int) { modint ret = *this; *this += 1; return ret; }
    modint operator--(int) { modint ret = *this; *this -= 1; return ret; }
    modint operator~() const { return (this -> pow(n, mod - 2)); } // inverse
    friend bool operator==(const modint& lhs, const modint& rhs) {
        return lhs.n == rhs.n;
    }
    friend bool operator<(const modint& lhs, const modint& rhs) {
        return lhs.n < rhs.n;
    }
    friend bool operator>(const modint& lhs, const modint& rhs) {
        return lhs.n > rhs.n;
    }
    friend modint &operator+=(modint& lhs, const modint& rhs) {
        lhs.n += rhs.n;
        if (lhs.n >= mod) lhs.n -= mod;
        return lhs;
    }
    friend modint &operator-=(modint& lhs, const modint& rhs) {
        lhs.n -= rhs.n;
        if (lhs.n < 0) lhs.n += mod;
        return lhs;
    }
    friend modint &operator*=(modint& lhs, const modint& rhs) {
        lhs.n = (lhs.n * rhs.n) % mod;
        return lhs;
    }
    friend modint &operator/=(modint& lhs, const modint& rhs) {
        lhs.n = (lhs.n * (~rhs).n) % mod;
        return lhs;
    }
    friend modint operator+(const modint& lhs, const modint& rhs) {
        return modint(lhs.n + rhs.n);
    }
    friend modint operator-(const modint& lhs, const modint& rhs) {
        return modint(lhs.n - rhs.n);
    }
    friend modint operator*(const modint& lhs, const modint& rhs) {
        return modint(lhs.n * rhs.n);
    }
    friend modint operator/(const modint& lhs, const modint& rhs) {
        return modint(lhs.n * (~rhs).n);
    }
};
istream& operator>>(istream& is, modint m) { is >> m.n; return is; }
ostream& operator<<(ostream& os, modint m) { os << m.n; return os; }

#define MAX_N 3030303
long long extgcd(long long a, long long b, long long& x, long long& y) {
    long long d = a;
    if (b != 0) {
        d = extgcd(b, a % b, y, x);
        y -= (a / b) * x;
    } else {
        x = 1; y = 0;
    }
    return d;
}
long long mod_inverse(long long a, long long m) {
    long long x, y;
    if(extgcd(a, m, x, y) == 1) return (m + x % m) % m;
    else return -1;
}
vector<long long> fact(MAX_N+1, inf);
long long mod_fact(long long n, long long& e) {
    if(fact[0] == inf) {
        fact[0]=1;
        if(MAX_N != 0) fact[1]=1;
        for(ll i = 2; i <= MAX_N; ++i) {
            fact[i] = (fact[i-1] * i) % mod;
        }
    }
    e = 0;
    if(n == 0) return 1;
    long long res = mod_fact(n / mod, e);
    e += n / mod;
    if((n / mod) % 2 != 0) return (res * (mod - fact[n % mod])) % mod;
    return (res * fact[n % mod]) % mod;
}
// return nCk
long long mod_comb(long long n, long long k) {
    if(n < 0 || k < 0 || n < k) return 0;
    long long e1, e2, e3;
    long long a1 = mod_fact(n, e1), a2 = mod_fact(k, e2), a3 = mod_fact(n - k, e3);
    if(e1 > e2 + e3) return 0;
    return (a1 * mod_inverse((a2 * a3) % mod, mod)) % mod;
}

using mi = modint;

int main() {
    ios::sync_with_stdio(false);
    cin.tie(0);
    int n, a, b, c;
    cin >> n >> a >> b >> c;
    if(b % 2) {
        cout << 0 << endl;
        return 0;
    }
    mi ans = 0;
    for(int i = a; i <= n; i++) {
        for(int j = 0; j <= i; j++) {
            int rem3 = c - (j + (i - a) * 3);
            if(rem3 < 0 || j > a) continue;
            mi tmp = mod_comb(i, a - j);
            tmp *= mod_comb(i - (a - j), j);
            if(b) {
                tmp *= mod_comb(i + 1 - 1 + b / 2, b / 2);
                tmp *= mod_comb(b / 2 - 1 + rem3, rem3);
            }
            if(!b && rem3) tmp = 0;
        #include <iostream>
#include <vector>
#include <queue>
#include <math.h>
#include <set>
#define FOR(i, n, m) for(ll i = n; i < (int)m; i++)
#define REP(i, n) FOR(i, 0, n)
#define ALL(v) v.begin(), v.end()
#define pb push_back
using namespace std;
using ll = std::int_fast64_t;
using P = pair<ll, ll>;
constexpr ll inf = 1000000000;
constexpr ll mod = 1000000007;
constexpr long double eps = 1e-15;
template<typename T1, typename T2>
ostream& operator<<(ostream& os, pair<T1, T2> p) {
    os << to_string(p.first) << " " << to_string(p.second);
    return os;
}
template<typename T>
ostream& operator<<(ostream& os, vector<T>& v) {
    REP(i, v.size()) {
        if(i) os << " ";
        os << to_string(v[i]);
    }
    return os;
}

struct modint {
    ll n;
public:
    modint(const ll n = 0) : n((n % mod + mod) % mod) {}
    static modint pow(modint a, int m) {
        modint r = 1;
        while(m > 0) {
            if(m & 1) { r *= a; }
            a = (a * a); m /= 2;
        }
        return r;
    }
    modint &operator++() { *this += 1; return *this; }
    modint &operator--() { *this -= 1; return *this; }
    modint operator++(int) { modint ret = *this; *this += 1; return ret; }
    modint operator--(int) { modint ret = *this; *this -= 1; return ret; }
    modint operator~() const { return (this -> pow(n, mod - 2)); } // inverse
    friend bool operator==(const modint& lhs, const modint& rhs) {
        return lhs.n == rhs.n;
    }
    friend bool operator<(const modint& lhs, const modint& rhs) {
        return lhs.n < rhs.n;
    }
    friend bool operator>(const modint& lhs, const modint& rhs) {
        return lhs.n > rhs.n;
    }
    friend modint &operator+=(modint& lhs, const modint& rhs) {
        lhs.n += rhs.n;
        if (lhs.n >= mod) lhs.n -= mod;
        return lhs;
    }
    friend modint &operator-=(modint& lhs, const modint& rhs) {
        lhs.n -= rhs.n;
        if (lhs.n < 0) lhs.n += mod;
        return lhs;
    }
    friend modint &operator*=(modint& lhs, const modint& rhs) {
        lhs.n = (lhs.n * rhs.n) % mod;
        return lhs;
    }
    friend modint &operator/=(modint& lhs, const modint& rhs) {
        lhs.n = (lhs.n * (~rhs).n) % mod;
        return lhs;
    }
    friend modint operator+(const modint& lhs, const modint& rhs) {
        return modint(lhs.n + rhs.n);
    }
    friend modint operator-(const modint& lhs, const modint& rhs) {
        return modint(lhs.n - rhs.n);
    }
    friend modint operator*(const modint& lhs, const modint& rhs) {
        return modint(lhs.n * rhs.n);
    }
    friend modint operator/(const modint& lhs, const modint& rhs) {
        return modint(lhs.n * (~rhs).n);
    }
};
istream& operator>>(istream& is, modint m) { is >> m.n; return is; }
ostream& operator<<(ostream& os, modint m) { os << m.n; return os; }

#define MAX_N 3030303
long long extgcd(long long a, long long b, long long& x, long long& y) {
    long long d = a;
    if (b != 0) {
        d = extgcd(b, a % b, y, x);
        y -= (a / b) * x;
    } else {
        x = 1; y = 0;
    }
    return d;
}
long long mod_inverse(long long a, long long m) {
    long long x, y;
    if(extgcd(a, m, x, y) == 1) return (m + x % m) % m;
    else return -1;
}
vector<long long> fact(MAX_N+1, inf);
long long mod_fact(long long n, long long& e) {
    if(fact[0] == inf) {
        fact[0]=1;
        if(MAX_N != 0) fact[1]=1;
        for(ll i = 2; i <= MAX_N; ++i) {
            fact[i] = (fact[i-1] * i) % mod;
        }
    }
    e = 0;
    if(n == 0) return 1;
    long long res = mod_fact(n / mod, e);
    e += n / mod;
    if((n / mod) % 2 != 0) return (res * (mod - fact[n % mod])) % mod;
    return (res * fact[n % mod]) % mod;
}
// return nCk
long long mod_comb(long long n, long long k) {
    if(n < 0 || k < 0 || n < k) return 0;
    long long e1, e2, e3;
    long long a1 = mod_fact(n, e1), a2 = mod_fact(k, e2), a3 = mod_fact(n - k, e3);
    if(e1 > e2 + e3) return 0;
    return (a1 * mod_inverse((a2 * a3) % mod, mod)) % mod;
}

using mi = modint;

int main() {
    ios::sync_with_stdio(false);
    cin.tie(0);
    int n, a, b, c;
    cin >> n >> a >> b >> c;
    if(b % 2) {
        cout << 0 << endl;
        return 0;
    }
    mi ans = 0;
    for(int i = a; i <= n; i++) {
        for(int j = 0; j <= i; j++) {
            int rem3 = c - (j + (i - a) * 3);
            if(rem3 < 0 || j > a) continue;
            mi tmp = mod_comb(i, a - j);
            tmp *= mod_comb(i - (a - j), j);
            if(b) {
                tmp *= mod_comb(i + 1 - 1 + b / 2, b / 2);
                tmp *= mod_comb(b / 2 - 1 + rem3, rem3);
            }
            if(!b && rem3) tmp = 0;
            ans += tmp;
        }
    }
    cout << ans << endl;
    return 0;
}
    ans += tmp;
        }
    }
    cout << ans << endl;
    return 0;
}


Compiler output:
a.cc:11:17: error: 'int_fast64_t' in namespace 'std' does not name a type
   11 | using ll = std::int_fast64_t;
      |                 ^~~~~~~~~~~~
a.cc:12:16: error: 'll' was not declared in this scope
   12 | using P = pair<ll, ll>;
      |                ^~
a.cc:12:20: error: 'll' was not declared in this scope
   12 | using P = pair<ll, ll>;
      |                    ^~
a.cc:12:22: error: template argument 1 is invalid
   12 | using P = pair<ll, ll>;
      |                      ^
a.cc:12:22: error: template argument 2 is invalid
a.cc:13:11: error: 'll' does not name a type
   13 | constexpr ll inf = 1000000000;
      |           ^~
a.cc:14:11: error: 'll' does not name a type
   14 | constexpr ll mod = 1000000007;
      |           ^~
a.cc: In function 'std::ostream& operator<<(std::ostream&, std::vector<_Tp>&)':
a.cc:6:26: error: 'll' was not declared in this scope
    6 | #define FOR(i, n, m) for(ll i = n; i < (int)m; i++)
      |                          ^~
a.cc:7:19: note: in expansion of macro 'FOR'
    7 | #define REP(i, n) FOR(i, 0, n)
      |                   ^~~
a.cc:23:5: note: in expansion of macro 'REP'
   23 |     REP(i, v.size()) {
      |     ^~~
a.cc:23:9: error: 'i' was not declared in this scope
   23 |     REP(i, v.size()) {
      |         ^
a.cc:6:36: note: in definition of macro 'FOR'
    6 | #define FOR(i, n, m) for(ll i = n; i < (int)m; i++)
      |                                    ^
a.cc:23:5: note: in expansion of macro 'REP'
   23 |     REP(i, v.size()) {
      |     ^~~
a.cc: At global scope:
a.cc:31:5: error: 'll' does not name a type
   31 |     ll n;
      |     ^~
a.cc:33:18: error: 'll' does not name a type
   33 |     modint(const ll n = 0) : n((n % mod + mod) % mod) {}
      |                  ^~
a.cc: In constructor 'modint::modint(int)':
a.cc:33:30: error: class 'modint' does not have any field named 'n'
   33 |     modint(const ll n = 0) : n((n % mod + mod) % mod) {}
      |                              ^
a.cc:33:37: error: 'mod' was not declared in this scope; did you mean 'modf'?
   33 |     modint(const ll n = 0) : n((n % mod + mod) % mod) {}
      |                                     ^~~
      |                                     modf
a.cc: In member function 'modint modint::operator~() const':
a.cc:46:52: error: 'n' was not declared in this scope; did you mean 'yn'?
   46 |     modint operator~() const { return (this -> pow(n, mod - 2)); } // inverse
      |                                                    ^
      |                                                    yn
a.cc:46:55: error: 'mod' was not declared in this scope; did you mean 'modf'?
   46 |     modint operator~() const { return (this -> pow(n, mod - 2)); } // inverse
      |                                                       ^~~
      |                                                       modf
a.cc: In function 'bool operator==(const modint&, const modint&)':
a.cc:48:20: error: 'const struct modint' has no member named 'n'
   48 |         return lhs.n == rhs.n;
      |                    ^
a.cc:48:29: error: 'const struct modint' has no member named 'n'
   48 |         return lhs.n == rhs.n;
      |                             ^
a.cc: In function 'bool operator<(const modint&, const modint&)':
a.cc:51:20: error: 'const struct modint' has no member named 'n'
   51 |         return lhs.n < rhs.n;
      |                    ^
a.cc:51:28: error: 'const struct modint' has no member named 'n'
   51 |         return lhs.n < rhs.n;
      |                            ^
a.cc: In function 'bool operator>(const modint&, const modint&)':
a.cc:54:20: error: 'const struct modint' has no member named 'n'
   54 |         return lhs.n > rhs.n;
      |                    ^
a.cc:54:28: error: 'const struct modint' has no member named 'n'
   54 |         return lhs.n > rhs.n;
      |                            ^
a.cc: In function 'modint& operator+=(modint&, const modint&)':
a.cc:57:13: error: 'struct modint' has no member named 'n'
   57 |         lhs.n += rhs.n;
      |             ^
a.cc:57:22: error: 'const struct modint' has no member named 'n'
   57 |         lhs.n += rhs.n;
      |                      ^
a.cc:58:17: error: 'struct modint' has no member named 'n'
   58 |         if (lhs.n >= mod) lhs.n -= mod;
      |                 ^
a.cc:58:22: error: 'mod' was not declared in this scope; did you mean 'modf'?
   58 |         if (lhs.n >= mod) lhs.n -= mod;
      |                      ^~~
      |                      modf
a.cc:58:31: error: 'struct modint' has no member named 'n'
   58 |         if (lhs.n >= mod) lhs.n -= mod;
      |                               ^
a.cc: In function 'modint& operator-=(modint&, const modint&)':
a.cc:62:13: error: 'struct modint' has no member named 'n'
   62 |         lhs.n -= rhs.n;
      |             ^
a.cc:62:22: error: 'const struct modint' has no member named 'n'
   62 |         lhs.n -= rhs.n;
      |                      ^
a.cc:63:17: error: 'struct modint' has no member named 'n'
   63 |         if (lhs.n < 0) lhs.n += mod;
      |                 ^
a.cc:63:28: error: 'struct modint' has no member named 'n'
   63 |         if (lhs.n < 0) lhs.n += mod;
      |                            ^
a.cc:63:33: error: 'mod' was not declared in this scope; did you mean 'modf'?
   63 |         if (lhs.n < 0) lhs.n += mod;
      |                                 ^~~
      |                                 modf
a.cc: In function 'modint& operator*=(modint&, const modint&)':
a.cc:67:13: error: 'struct modint' has no member named 'n'
   67 |         lhs.n = (lhs.n * rhs.n) % mod;
      |             ^
a.cc:67:22: error: 'struct modint' has no member named 'n'
   67 |         lhs.n = (lhs.n * rhs.n) % mod;
      |                      ^
a.cc:67:30: error: 'const struct modint' has no member named 'n'
   67 |         lhs.n = (lhs.n * rhs.n) % mod;
      |                              ^
a.cc:67:35: error: 'mod' was not declared in this scope; did you mean 'modf'?
   67 |         lhs.n = (lhs.n * rhs.n) % mod;
      |                                   ^~~
      |                                   modf
a.cc: In function 'modint& operator/=(modint&, const modint&)':
a.cc:71:13: error: 'struct modint' has no member named 'n'
   71 |         lhs.n = (lhs.n * (~rhs).n) % mod;
      |             ^
a.cc:71:22: error: 'struct modint' has no member named 'n'
   71 |         lhs.n = (lhs.n * (~rhs).n) % mod;
      |                      ^
a.cc:71:33: error: 'struct modint' has no member named 'n'
   71 |         lhs.n = (lhs.n * (~rhs).n) % mod;
      |                                 ^
a.cc:71:38: error: 'mod' was not declared in this scope; did you mean 'modf'?
   71 |         lhs.n = (lhs.n * (~rhs).n) % mod;
      |                                      ^~~
      |                                      modf
a.cc: In function 'modint operator+(const modint&, const modint&)':
a.cc:75:27: error: 'const struct modint' has no member named 'n'
   75 |         return modint(lhs.n + rhs.n);
      |                           ^
a.cc:75:35: error: 'const struct modint' has no member named 'n'
   75 |         return modint(lhs.n + rhs.n);
      |                                   ^
a.cc: In function 'modint operator-(const modint&, const modint&)':
a.cc:78:27: error: 'const struct modint' has no member named 'n'
   78 |         return modint(lhs.n - rhs.n);
      |                           ^
a.cc:78:35: error: 'const struct modint' has no member named 'n'
   78 |         return modint(lhs.n - rhs.n);
      |                                   ^
a.cc: In function 'modint operator*(const modint&, const modint&)':
a.cc:81:27: error: 'const struct modint' has no member named 'n'
   81 |         return modint(lhs.n * rhs.n);
      |                           ^
a.cc:81:35: error: 'const struct modint' has no member named 'n'
   81 |         return modint(lhs.n * rhs.n);
      |                                   ^
a.cc: In function 'modint operator/(const modint&, const modint&)':
a.cc:84:27: error: 'const struct modint' has no member named 'n'
   84 |         return modint(lhs.n * (~rhs).n);
      |                           ^
a.cc:84:38: error: 'struct modint' has no member named 'n'
   84 |         return modint(lhs.n * (~rhs).n);
      |                                      ^
a.cc: In function 'std::istream& operator>>(std::istream&, modint)':
a.cc:87:54: error: 'struct modint' has no member named 'n'
   87 | istream& operator>>(istream& is, modint m) { is >> m.n; return is; }
      |                                                      ^
a.cc: In function 'std::ostream& operator<<(std::ostream&, modint)':
a.cc:88:54: error: 'struct modint' has no member named 'n'
   88 | ostream& operator<<(ostream& os, modint m) { os << m.n; return os; }
      |                                                      ^
a.cc: At global scope:
a.cc:106:33: error: 'inf' was not declared in this scope; did you mean 'ynf'?
  106 | vector<long long> fact(MAX_N+1, inf);
      |                                 ^~~
      |                                 ynf
a.cc: In function 'long long int mod_fact(long long int, long long int&)':
a.cc:108:19: error: 'inf' was not declared in this scope; did you mean 'ynf'?
  108 |     if(fact[0] == inf) {
      |                   ^~~
      |                   ynf
a.cc:111:13: error: 'll' was not declared in this scope
  111 |         for(ll i = 2; i <= MAX_N; ++i) {
      |             ^~
a.cc:111:23: error: 'i' was not declared in this scope
  111 |         for(ll i = 2; i <= MAX_N; ++i) {
      |                       ^
a.cc:112:41: error: 'mod' was not declared in this scope; did you mean 'modf'?
  112 |             fact[i] = (fact[i-1] * i) % mod;
      |                                         ^~~
      |                                         modf
a.cc:117:34: error: 'mod' was not declared in this scope; did you mean 'modf'?
  117 |     long long res = mod_fact(n / mod, e);
      |                                  ^~~
      |                                  modf
a.cc: In function 'long long int mod_comb(long long int, long long int)':
a.cc:128:42: error: 'mod' was not declared in this scope; did you mean 'modf'?
  12