/** * author: otera * created: 17.09.2021 22:51:47 **/ #include #include using namespace std; using ll = long long; using ld = long double; using ull = unsigned long long; using uint = unsigned; #define repa(i, n) for(int i = 0; i < n; ++ i) #define repb(i, a, b) for(int i = a; i < b; ++ i) #define repc(i, a, b, c) for(int i = a; i < b; i += c) #define overload4(a, b, c, d, e, ...) e #define rep(...) overload4(__VA_ARGS__, repc, repb, repa)(__VA_ARGS__) #define rep1a(i, n) for(int i = 0; i <= n; ++ i) #define rep1b(i, a, b) for(int i = a; i <= b; ++ i) #define rep1c(i, a, b, c) for(int i = a; i <= b; i += c) #define rep1(...) overload4(__VA_ARGS__, rep1c, rep1b, rep1a)(__VA_ARGS__) #define per(i,n) for(int i=n-1;i>=0;i--) #define per1(i,n) for(int i=n;i>=1;i--) typedef pair P; typedef pair LP; #define pb push_back #define eb emplace_back #define fr first #define sc second #define all(c) c.begin(),c.end() #define lb(c, x) distance((c).begin(), lower_bound(all(c), (x))) #define ub(c, x) distance((c).begin(), upper_bound(all(c), (x))) #define Sort(a) sort(all(a)) #define Rev(a) reverse(all(a)) #define Uniq(a) sort(all(a));a.erase(unique(all(a)),end(a)) #define si(c) (int)(c).size() inline ll popcnt(ull a){ return __builtin_popcountll(a); } #define tpow(n) (1LL<<(n)) #define unless(A) if(!(A)) ll intpow(ll a, ll b){ ll ans = 1; while(b){ if(b & 1) ans *= a; a *= a; b /= 2; } return ans; } ll intpow(ll a, ll b, ll m) {ll ans = 1; while(b){ if(b & 1) (ans *= a) %= m; (a *= a) %= m; b /= 2; } return ans; } template inline bool chmax(T& a, T b) { if (a < b) { a = b; return 1; } return 0; } template inline bool chmin(T& a, T b) { if (a > b) { a = b; return 1; } return 0; } #define INT(...) int __VA_ARGS__;in(__VA_ARGS__) #define LL(...) ll __VA_ARGS__;in(__VA_ARGS__) #define ULL(...) ull __VA_ARGS__;in(__VA_ARGS__) #define STR(...) string __VA_ARGS__;in(__VA_ARGS__) #define CHR(...) char __VA_ARGS__;in(__VA_ARGS__) #define DBL(...) double __VA_ARGS__;in(__VA_ARGS__) #define LD(...) ld __VA_ARGS__;in(__VA_ARGS__) #define vec(type,name,...) vectorname(__VA_ARGS__) #define VEC(type,name,size) vectorname(size);in(name) #define vv(type,name,h,...) vector>name(h,vector(__VA_ARGS__)) #define VV(type,name,h,w) vector>name(h,vector(w));in(name) #define vvv(type,name,h,w,...) vector>>name(h,vector>(w,vector(__VA_ARGS__))) template using vc = vector; template using vvc = vector>; template using vvvc = vector>; template using vvvvc = vector>; template using pq = priority_queue; template using pqg = priority_queue, greater>; template void scan(T& a){ cin >> a; } template void scan(vector& a){ for(auto&& i : a) scan(i); } void in(){} template void in(Head& head, Tail&... tail){ scan(head); in(tail...); } void print(){ cout << ' '; } template void print(const T& a){ cout << a; } template void print(const vector& a){ if(a.empty()) return; print(a[0]); for(auto i = a.begin(); ++i != a.end(); ){ cout << ' '; print(*i); } } int out(){ cout << '\n'; return 0; } template int out(const T& t){ print(t); cout << '\n'; return 0; } template int out(const Head& head, const Tail&... tail){ print(head); cout << ' '; out(tail...); return 0; } #define CHOOSE(a) CHOOSE2 a #define CHOOSE2(a0,a1,a2,a3,a4,x,...) x #define debug_1(x1) cout<<#x1<<": "< struct BiCoef { vector fact_, inv_, finv_; int MOD = T::mod(); constexpr BiCoef() {} constexpr BiCoef(int n) noexcept : fact_(n, 1), inv_(n, 1), finv_(n, 1) { init(n); } constexpr void init(int n) noexcept { fact_.assign(n, 1), inv_.assign(n, 1), finv_.assign(n, 1); for(int i = 2; i < n; i++){ fact_[i] = fact_[i-1] * i; inv_[i] = -inv_[MOD%i] * (MOD/i); finv_[i] = finv_[i-1] * inv_[i]; } } constexpr T com(int n, int k) const noexcept { if(n == k) return 1; if(k == 0) return 1; if (n < k || n < 0 || k < 0) return 0; return fact_[n] * finv_[k] * finv_[n-k]; } constexpr T fact(int n) const noexcept { if (n < 0) return 0; return fact_[n]; } constexpr T inv(int n) const noexcept { if (n < 0) return 0; return inv_[n]; } constexpr T finv(int n) const noexcept { if (n < 0) return 0; return finv_[n]; } }; BiCoef bc; // // a_0 + ... + a_{k - 1} = n // mint H(int n, int k) { // return bc.com(n + k - 1, k); // } void solve() { bc.init(2000200); INT(a, b, x, y); if((a + x + y) % 2 != 0) { out(0); return; } vc cnt(4, 0); for(int i = 0; i <= b; ++ i) cnt[i % 4] ++; mint ans = 0; for(int cxp = 0; cxp <= (a + x + y) / 2; ++ cxp) { int cyp = (a + x + y) / 2 - cxp; int cxm = cxp - x; int cym = cyp - y; if(cxm < 0 or cym < 0) continue; debug(cnt[0], cnt[1], cnt[2], cnt[3]); debug(cxp, cyp, cxm, cym); debug(ans.val()); ans += bc.com(cnt[0] + cxp - 1, cxp) * bc.com(cnt[1] + cyp - 1, cyp) * bc.com(cnt[2] + cxm - 1, cxm) * bc.com(cnt[3] + cym - 1, cym); } out(ans.val()); } signed main() { ios::sync_with_stdio(false); cin.tie(0); // cout << fixed << setprecision(20); // INT(t); rep(i, t)solve(); solve(); return 0; }