Problem:
Score : 600 points

Problem Statement

Snuke is standing on a two-dimensional plane. In one operation, he can move by 1 in the positive x-direction, or move by 1 in the positive y-direction.

Let us define a function f(r, c) as follows:

f(r,c) := (The number of paths from the point (0, 0) to the point (r, c) that Snuke can trace by repeating the operation above)

Given are integers r_1, r_2, c_1, and c_2.
Find the sum of f(i, j) over all pair of integers (i, j) such that r_1 ≤ i ≤ r_2 and c_1 ≤ j ≤ c_2, and compute this value modulo (10^9+7).

Constraints

1 ≤ r_1 ≤ r_2 ≤ 10^6

1 ≤ c_1 ≤ c_2 ≤ 10^6

All values in input are integers.

Input

Input is given from Standard Input in the following format:

r_1 c_1 r_2 c_2

Output

Print the sum of f(i, j) modulo (10^9+7).

Sample Input 1

1 1 2 2

Sample Output 1

14

For example, there are two paths from the point (0, 0) to the point (1, 1): (0,0) → (0,1) → (1,1) and (0,0) → (1,0) → (1,1), so f(1,1)=2.

Similarly, f(1,2)=3, f(2,1)=3, and f(2,2)=6. Thus, the sum is 14.

Sample Input 2

314 159 2653 589

Sample Output 2

602215194

Solution in C++14 (GCC 5.4.1) (judge verdict: Time Limit Exceeded)

#pragma GCC target("avx2")
#pragma GCC optimization("O3")
#pragma GCC optimization("unroll-loops")
#include <algorithm>
#include <assert.h>
#include <bitset>
#include <cfloat>
#include <complex>
#include <deque>
#include <fstream>
#include <functional>
#include <iomanip>
#include <iostream>
#include <limits.h>
#include <list>
#include <map>
#include <math.h>
#include <queue>
#include <random>
#include <set>
#include <stack>
#include <string>
#include <string.h>
#include <time.h>
#include <unordered_map>
#include <unordered_set>
#include <vector>
#define rep(i,n) for(int i=0;i<n;i++)
#define REP(i,n) for(int i=1;i<=n;i++)
#define int long long
#define ll long long
#define eps LDBL_EPSILON
#define mod (int)1000000007
#ifdef int
#define INF LLONG_MAX/10
#else
#define INF INT_MAX/10
#endif
#define DBLINF (DBL_MAX)/10
#define P pair<int,int>
#define prique(T) priority_queue<T,vector<T>,greater<T>>
#define all(V) V.begin(),V.end()
template <class T, class U>
inline bool chmax(T& lhs, const U& rhs) {
	if (lhs < rhs) {
		lhs = rhs;
		return 1;
	}
	return 0;
}
template <class T, class U>
inline bool chmin(T& lhs, const U& rhs) {
	if (lhs > rhs) {
		lhs = rhs;
		return 1;
	}
	return 0;
}
using namespace std;
inline int gcd(int a, int b) {
	while (b) {
		int c = a;
		a = b; b = c % b;
	}
	return a;
}
inline int lcm(int a, int b) {
	return a / gcd(a, b) * b;
}
bool isprime(int n) {
	if (n == 1)return false;
	for (int i = 2; i * i <= n; i++) {
		if (n % i == 0)return false;
	}
	return true;
}
int mypow(int a, int b) {
	if (!b)return 1;
	if (b & 1)return mypow(a, b - 1) * a;
	int memo = mypow(a, b >> 1);
	return memo * memo;
}
int modpow(int a, int b, int m = mod) {
	if (!b)return 1;
	if (b & 1)return modpow(a, b - 1, m) * a % m;
	int memo = modpow(a, b / 2, m);
	return memo * memo % m;
}
class modInt {
	int value, modulo;
public:
	modInt() : value(0), modulo(mod) { value = 0; }
	template<typename T>
	modInt(T value = 0, int modulo = mod) : value(value), modulo(modulo) {
		if (value < 0) {
			value = -value;
			value %= modulo;
			value = -value;
			value += modulo;
		}
		this->value = value % modulo;
	}
	inline operator int()const { return value; }
	inline modInt& operator+=(modInt x) {
		value += x.value;
		if (value >= modulo)value -= modulo;
		return *this;
	}
	inline modInt& operator++() {
		if (value == modulo - 1)value = 0;
		else value++;
		return *this;
	}
	inline modInt& operator-()const {
		return modInt(0) -= *this;
	}
	inline modInt& operator-=(modInt x) {
		value -= x.value;
		if (value < 0)value += modulo;
		return *this;
	}
	inline modInt& operator--() {
		if (value == 0)value = modulo - 1;
		else value--;
		return *this;
	}
	inline modInt& operator*=(modInt x) {
		value = value * x.value % modulo;
		return *this;
	}
	inline modInt& operator/=(modInt x) {
		return operator*=(x.inv());
	}
	inline modInt inv() {
		return modpow(*this, modulo - 2);
	}
	template<typename T> modInt operator+(T x) { return modInt(*this) += x; }
	template<typename T> modInt& operator+=(T x) { return operator+=(modInt(x, modulo)); }
	template<typename T> modInt operator-(T x) { return modInt(*this) -= x; }
	template<typename T> modInt& operator-=(T x) { return operator-=(modInt(x, modulo)); }
	template<typename T> modInt operator*(T x) { return modInt(*this) *= x; }
	template<typename T> modInt& operator*=(T x) { return operator*=(modInt(x, modulo)); }
	template<typename T> modInt operator/(T x) { return modInt(*this) /= x; }
	template<typename T> modInt& operator/=(T x) { return operator/=(modInt(x, modulo)); }
};
istream& operator>>(istream& ist, modInt& x) {
	int a;
	ist >> a;
	x = a;
	return ist;
}
modInt modpow(modInt a, int b) {
	if (!b)return modInt(1);
	if (b & 1)return modpow(a, b - 1) * a;
	modInt memo = modpow(a, b / 2);
	return memo * memo;
}
class UnionFind {
protected:
	int* par, * rank, * size;
public:
	UnionFind(unsigned int size) {
		par = new int[size];
		rank = new int[size];
		this->size = new int[size];
		rep(i, size) {
			par[i] = i;
			rank[i] = 0;
			this->size[i] = 1;
		}
	}
	int find(int n) {
		if (par[n] == n)return n;
		return par[n] = find(par[n]);
	}
	void unite(int n, int m) {
		n = find(n);
		m = find(m);
		if (n == m)return;
		if (rank[n] < rank[m]) {
			par[n] = m;
			size[m] += size[n];
		}
		else {
			par[m] = n;
			size[n] += size[m];
			if (rank[n] == rank[m])rank[n]++;
		}
	}
	bool same(int n, int m) {
		return find(n) == find(m);
	}
	int getsize(int n) {
		return size[find(n)];
	}
};
class PersistantUnionFind :UnionFind {
	P* notparent;
	vector<P>* sizevec;
	int opcount = 0;
public:
	PersistantUnionFind(unsigned int size) :UnionFind(size) {
		this->sizevec = new vector<P>[size];
		notparent = new P[size];
		rep(i, size) {
			par[i] = i;
			rank[i] = 0;
			sizevec[i].push_back(make_pair(-1, 1));
			notparent[i] = make_pair(INF, i);
		}
	}
	int find(int n, int t = INF) {
		if (opcount <= t) {
			if (par[n] == n)return n;
			return par[n] = find(par[n]);
		}
		if (notparent[n].first <= t)return find(notparent[n].second, t);
		return n;
	}
	void unite(int n, int m) {
		n = find(n);
		m = find(m);
		if (n == m) {
			opcount++;
			return;
		}
		if (rank[n] < rank[m]) {
			par[n] = m;
			notparent[n] = make_pair(opcount, m);
			sizevec[m].push_back(make_pair(opcount, sizevec[m].back().second + sizevec[n].back().second));
		}
		else {
			par[m] = n;
			notparent[m] = make_pair(opcount, n);
			sizevec[n].push_back(make_pair(opcount, sizevec[n].back().second + sizevec[m].back().second));
			if (rank[n] == rank[m])rank[n]++;
		}
		opcount++;
	}
	bool same(int n, int m, int t = INF) {
		return find(n, t) == find(m, t);
	}
	int getsize(int n, int t = INF) {
		n = find(n, t);
		auto ite = lower_bound(sizevec[n].begin(), sizevec[n].end(), make_pair(t, (int)0));
		if (ite == sizevec[n].end())ite--;
		if (t < (*ite).first)ite--;
		return (*ite).second;
	}
};
class RollingHash {
	string s;
	int n, m;
	modInt base;
	vector<modInt> has, power;
public:
	RollingHash(string s, int m, int b) : n(s.size()), m(m), base(b, m) { init(s, m, b); }
	void init(string s, int m, int b) {
		n = s.size();
		has.resize(n);
		power.resize(n);
		base = modInt(b, m);
		this->s = s;
		this->m = m;
		rep(i, n) {
			has[i] = modInt(s[i], m);
			if (i) {
				has[i] += base * has[i - 1];
				power[i] = power[i - 1] * base;
			}
			else power[i] = 1;
		}
	}
	operator int() const {
		return has.back();
	}
	int query(int a, int b) {
		assert(!(a >= b || a < 0 || n < b));
		return has[b - 1] - power[b - a] * (!a ? modInt(0) : has[a - 1]);
	}
	RollingHash& operator+=(string t) {
		s += t;
		has.resize(n + t.size());
		power.resize(n + t.size());
		for (int i = n; i < n + t.size(); i++) {
			has[i] = modInt(t[i] * base, m);
			has[i] += base * has[i - 1];
			power[i] = power[i - 1] * base;
		}
		n += t.size();
		return *this;
	}
};
template<typename T, typename U>
class SegTree {
	int n = 1;
	T* node = NULL;
	U* lazy = NULL;
	bool* lazyflag = NULL;
	T nodee;
	function<T(T, T)> nodef;
	function<U(U, U)> lazyf;
	function<T(T, U, int, int)> updf;
	void eval(int k, int l, int r) {
		if (lazyflag[k]) {
			node[k] = updf(node[k], lazy[k], l, r);
			if (r - l > 1) {
				if (lazyflag[2 * k + 1])lazy[2 * k + 1] = lazyf(lazy[2 * k + 1], lazy[k]);
				else lazy[2 * k + 1] = lazy[k];
				if (lazyflag[2 * k + 2])lazy[2 * k + 2] = lazyf(lazy[2 * k + 2], lazy[k]);
				else lazy[2 * k + 2] = lazy[k];
				lazyflag[2 * k + 1] = lazyflag[2 * k + 2] = true;
			}
			lazyflag[k] = false;
		}
	}
public:
	SegTree(int m, T init, T nodee, function<T(T, T)> nodef, function<U(U, U)> lazyf, function<T(T, U, int, int)> updf) :nodee(nodee), nodef(nodef), lazyf(lazyf), updf(updf) {
		delete[] node;
		delete[] lazy;
		while (n < m)n *= 2;
		node = new T[2 * n], lazy = new U[2 * n], lazyflag = new bool[2 * n];
		for (int i = n - 1; i < 2 * n - 1; i++)node[i] = init;
		for (int i = n - 2; i >= 0; i--)node[i] = nodef(node[2 * i + 1], node[2 * i + 2]);
		rep(i, 2 * n)lazyflag[i] = false;
	}
	SegTree(int m, T nodee, function<T(T, T)> nodef, function<U(U, U)> lazyf, function<T(T, U, int, int)> updf, vector<T> initvec) :nodee(nodee), nodef(nodef), lazyf(lazyf), updf(updf) {
		if (m != initvec.size()) {
			cerr << "Invalid Initialization of SegmentTree" << endl;
			exit(1);
		}
		delete[] node;
		delete[] lazy;
		while (n < m)n *= 2;
		node = new T[2 * n], lazy = new U[2 * n], lazyflag = new bool[2 * n];
		for (int i = n - 1; i < 2 * n - 1; i++) {
			if (i - n + 1 < m)node[i] = initvec[i - n + 1];
			else node[i] = nodee;
		}
		for (int i = n - 2; i >= 0; i--)node[i] = nodef(node[2 * i + 1], node[2 * i + 2]);
		rep(i, 2 * n)lazyflag[i] = false;
	}
	~SegTree() {
		delete[] node;
		delete[] lazy;
	}
	void update(int a, int b, U x, int k = 0, int l = 0, int r = -1) {
		if (r == -1)r = n;
		eval(k, l, r);
		if (b <= l || r <= a)return;
		if (a <= l && r <= b) {
			lazyflag[k] = true;
			lazy[k] = x;
			eval(k, l, r);
		}
		else {
			update(a, b, x, 2 * k + 1, l, (l + r) / 2);
			update(a, b, x, 2 * k + 2, (l + r) / 2, r);
			node[k] = nodef(node[2 * k + 1], node[2 * k + 2]);
		}
	}
	T query(int a, int b, int k = 0, int l = 0, int r = -1) {
		if (r == -1)r = n;
		eval(k, l, r);
		if (b <= l || r <= a)return nodee;
		if (a <= l && r <= b)return node[k];
		T vl = query(a, b, 2 * k + 1, l, (l + r) / 2);
		T vr = query(a, b, 2 * k + 2, (l + r) / 2, r);
		return nodef(vl, vr);
	}
};
template<typename T>
class RAQRSQ :public SegTree<T, T> {
public:
	RAQRSQ(int size, const T& def = T()) :SegTree<T, T>(size, def, T(), [](T a, T b) {return a + b; }, [](T a, T b) {return a + b; }, [](T a, T b, int l, int r) {return a + (r - l) * b; }) {};
};
template<typename T>
class RAQRMiQ :public SegTree<T, T> {
public:
	RAQRMiQ(int size, const T& def = T()) :SegTree<T, T>(size, def, INF, [](T a, T b) {return min(a, b); }, [](T a, T b) {return a + b; }, [](T a, T b, int l, int r) {return a + b; }) {};
};
template<typename T>
class RAQRMaQ :public SegTree<T, T> {
	using base = SegTree<T, T>;
public:
	RAQRMaQ(int size, const T& def = T()) :base(size, def, -INF, [](T a, T b) {return max(a, b); }, [](T a, T b) {return a + b; }, [](T a, T b, int l, int r) {return a + b; }) {};
};
template<typename T>
class RUQRSQ :public SegTree<T, T> {
	using base = SegTree<T, T>;
public:
	RUQRSQ(int size, const T& def = T()) :base(size, def, T(), [](T a, T b) {return a + b; }, [](T a, T b) {return b; }, [](T a, T b, int l, int r) {return (r - l) * b; }) {};
};
template<typename T>
class RUQRMiQ :public SegTree<T, T> {
	using base = SegTree<T, T>;
public:
	RUQRMiQ(int size, const T& def = T()) :base(size, def, T(), [](T a, T b) {return min(a, b); }, [](T a, T b) {return b; }, [](T a, T b, int l, int r) {return b; }) {};
};
template<typename T>
class RUQRMaQ :public SegTree<T, T> {
	using base = SegTree<T, T>;
public:
	RUQRMaQ(int size, const T& def = T()) :base(size, def, T(), [](T a, T b) {return max(a, b); }, [](T a, T b) {return b; }, [](T a, T b, int l, int r) {return b; }) {};
};
class BIT {
	int n;
	int* bit;
public:
	BIT(int n) :n(n) {
		bit = new int[n];
		fill(bit + 1, bit + n + 1, 0);
	}
	void add(int a, int x) {
		while (a <= n) {
			bit[a] += x;
			a += a & -a;
		}
	}
	int query(int a) {
		int cnt = 0;
		while (a > 0) {
			cnt += bit[a];
			a -= a & -a;
		}
		return cnt;
	}
};
class ConvexHullTrick {
	bool minOrMax, lineMonotone;
	class Line {
	public:
		int a, b;
		bool isquery;
		mutable std::function<const Line * ()> getSuc;
		bool operator<(const Line& x) const {
			if (isquery) {
				const Line* suc = next(this);
				if (suc == nullptr) return true;
				return (suc->a - x.a) * a + suc->b - x.b > 0;
			}
			if (x.isquery) {
				const Line* suc = next(this);
				if (suc == nullptr) return false;
				return (suc->a - a) * x.a + suc->b - b < 0;
			}
			return a < x.a;
		}
	};
	bool isbad(const set<Line>::iterator x) {
		if (x == st.begin() || next(x) == st.end())return false;
		auto pre = prev(x), nex = next(x);
		if (((*x).b - (*pre).b) * ((*nex).a - (*x).a) >= ((*nex).b - (*x).b) * ((*x).a - (*pre).a))return true;
		return false;
	}
	bool isbad(const vector<Line>::iterator x) {
		if (x == vec.begin() || next(x) == vec.end())return false;
		auto pre = prev(x), nex = next(x);
		if (((*x).b - (*pre).b) * ((*nex).a - (*x).a) >= ((*nex).b - (*x).b) * ((*x).a - (*pre).a))return true;
		return false;
	}
	set<Line> st;
	vector<Line> vec;
public:
	ConvexHullTrick(bool minormax = false, bool lineMonotone = false) :minOrMax(minormax), lineMonotone(lineMonotone) {}
	void addLine(int a, int b) {
		if (minOrMax) {
			a = -a; b = -b;
		}
		if (!lineMonotone) {
			auto pos = st.lower_bound({ a,-INF,false });
			if (pos != st.end()) {
				if ((*pos).a == a) {
					if ((*pos).b <= b)return;
					st.erase(pos);
				}
			}
			auto ite = st.insert({ a,b,false }).first;
			ite->getSuc = [=] {return next(ite) == st.end() ? nullptr : &*next(ite); };
			if (isbad(ite)) {
				st.erase(ite);
				return;
			}
			while (next(ite) != st.end() && isbad(next(ite)))st.erase(next(ite));
			while (ite != st.begin() && isbad(prev(ite)))st.erase(prev(ite));
		}
		else {
			if (!vec.empty()) {
				if (vec.back().a > a) {
					cerr << "Line additions are not monotone" << endl;
					exit(1);
				}
				if (vec.back().a == a) {
					if (vec.back().b <= b)return;
					vec.pop_back();
				}
			}
			vec.push_back({ a,b,false });
			auto ite = --vec.end();
			int index = vec.size() - 1;
			ite->getSuc = [this, index] {cout << vec.size() << endl; return index == vec.size() - 1 ? nullptr : &*(vec.begin() + index + 1); };
			while (ite != vec.begin() && isbad(prev(ite))) {
				*prev(ite) = vec.back();
				vec.pop_back();
				ite = --vec.end();
			}
		}
	}
	int query(int x) {
		if (!lineMonotone) {
			auto l = *st.lower_bound(Line{ x, 0,true });
			if (!minOrMax)return l.a * x + l.b;
			else return -l.a * x - l.b;
		}
		else {
			auto l = *lower_bound(vec.begin(), vec.end() - 1, Line({ x,0,true }));
			if (!minOrMax)return l.a * x + l.b;
			else return -l.a * x - l.b;
		}
	}
};
template<typename T>
class Matrix {
	int n;
	T zero, e;
	vector<vector<T>> vec;
	void letmeasure() {
		rep(i, n) {
			rep(j, n) {
				if (i != j)vec[i][j] = zero;
				else vec[i][j] = e;
			}
		}
	}
public:
	Matrix(int n, T zero, T e) :n(n), zero(zero), e(e) {
		vec.resize(n, vector<T>(n));
	}
	Matrix(int n, T zero, T e, vector<int> vec) :n(n), zero(zero), e(e) {
		if (vec.size() != n * n) {
			cerr << "Invalid construct of matrix" << endl;
			exit(1);
		}
		this->vec.resize(n, vector<T>(n));
		rep(i, n) {
			rep(j, n)this->vec[i][j] = vec[i * n + j];
		}
	}
	T& operator[](int a) {
		return vec[a / n][a % n];
	}
	unsigned int size() { return n; }
	Matrix operator*(const Matrix& a) {
		if (this->n != a.n || this->zero != a.zero || this->e != a.e) {
			cerr << "Invalid multiply of matrix" << endl;
			exit(1);
		}
		Matrix<T> res(n, zero, e);
		rep(i, n) {
			rep(j, n) {
				res.vec[i][j] = zero;
				rep(k, n) {
					chmin(res.vec[i][j], vec[i][k] + a.vec[k][j]);
				}
			}
		}
		return res;
	}
	static Matrix<T> measure(int n, T zero, T e) {
		Matrix<T> res(n, zero, e);
		res.letmeasure();
		return res;
	}
	static Matrix<T> mypow(Matrix<T> a, int b) {
		if (!b)return Matrix<T>::measure(a.size(), a.zero, a.e);
		if (b % 2)return mypow(a, b - 1) * a;
		Matrix<T> memo = mypow(a, b / 2);
		return memo * memo;
	}
};
class mycomplex {
	double realvalue, imagvalue;
public:
	mycomplex() :realvalue(0), imagvalue(0) {}
	mycomplex(double realvalue, double imagvalue) : realvalue(realvalue), imagvalue(imagvalue) {}
	mycomplex(double realvalue) : realvalue(realvalue), imagvalue(0) {}
	mycomplex(complex<double> c) :realvalue(c.real()), imagvalue(c.imag()) {}
	mycomplex(const mycomplex& rhs) :realvalue(rhs.realvalue), imagvalue(rhs.imagvalue) {}
	double real()const { return this->realvalue; }
	double imag()const { return this->imagvalue; }
	double abs() { return hypot(realvalue, imagvalue); }
	mycomplex& operator=(const mycomplex& obj) {
		if (this != &obj) {
			this->realvalue = obj.realvalue;
			this->imagvalue = obj.imagvalue;
		}
		return *this;
	}
	mycomplex& operator=(mycomplex&& obj)noexcept {
		if (this != &obj) {
			this->realvalue = exchange(obj.realvalue, 0);
			this->imagvalue = exchange(obj.imagvalue, 0);
		}
		return *this;
	}
	mycomplex& operator+=(const mycomplex& rhs) {
		this->realvalue += rhs.realvalue;
		this->imagvalue += rhs.imagvalue;
		return *this;
	}
	friend mycomplex operator+(mycomplex lhs, const mycomplex& rhs) {
		lhs += rhs;
		return lhs;
	}
	mycomplex& operator-=(const mycomplex& rhs) {
		this->realvalue -= rhs.realvalue;
		this->imagvalue -= rhs.imagvalue;
		return *this;
	}
	mycomplex& operator-=(const double& rhs) {
		this->realvalue -= rhs;
		return *this;
	}
	friend mycomplex operator-(mycomplex lhs, const mycomplex& rhs) {
		lhs -= rhs;
		return lhs;
	}
	mycomplex& operator*=(const mycomplex& rhs) {
		double pastreal = this->realvalue;
		this->realvalue = this->realvalue * rhs.realvalue - this->imagvalue * rhs.imagvalue;
		this->imagvalue = pastreal * rhs.imagvalue + rhs.realvalue * this->imagvalue;
		return *this;
	}
	friend mycomplex operator*(mycomplex lhs, const mycomplex& rhs) {
		lhs *= rhs;
		return lhs;
	}
	mycomplex& operator/=(const mycomplex& rhs) {
		*this *= mycomplex(rhs.real(), -rhs.imag());
		double dnm = rhs.real() * rhs.real() - rhs.imag() * rhs.imag();
		this->realvalue /= dnm;
		this->imagvalue /= dnm;
		return *this;
	}
	friend mycomplex operator/(mycomplex lhs, const mycomplex& rhs) {
		lhs /= rhs;
		return lhs;
	}
};
class FastFourierTransform {
private:
	static void dft(vector<mycomplex>& func, int inverse) {
		int sz = func.size();
		if (sz == 1)return;
		vector<mycomplex> veca, vecb;
		rep(i, sz / 2) {
			veca.push_back(func[2 * i]);
			vecb.push_back(func[2 * i + 1]);
		}
		dft(veca, inverse); dft(vecb, inverse);
		mycomplex now = 1, zeta = polar(1.0, inverse * 2.0 * acos(-1) / sz);
		rep(i, sz) {
			func[i] = veca[i % (sz / 2)] + now * vecb[i % (sz / 2)];
			now *= zeta;
		}
	}
public:
	template<typename T>
	static vector<double> multiply(vector<T> f, vector<T> g) {
		vector<mycomplex> nf, ng;
		int sz = 1;
		while (sz < f.size() + g.size())sz *= 2;
		nf.resize(sz); ng.resize(sz);
		rep(i, f.size()) {
			nf[i] = f[i];
			ng[i] = g[i];
		}
		dft(nf, 1);
		dft(ng, 1);
		rep(i, sz)nf[i] *= ng[i];
		dft(nf, -1);
		vector<double> res;
		rep(i, sz)res.push_back(nf[i].real() / sz);
		return res;
	}
};
int x, y, z, w;
modInt k[2000010];
modInt comb(int a, int b) {
	return k[a] / k[a - b] / k[b];
}
signed main() {
	cin >> x >> z >> y >> w;
	int r = y - x + 1, c = w - z + 1;
	k[0] = 1;
	REP(i, 2000009) {
		k[i] = k[i - 1] * i;
	}
	modInt ans = 0, now = comb(c, c - 1);
	for (int i = y; i >= x; i--) {
		ans += now * comb(z + i - 1, z - 1);
		now += comb(c + (y - i) + 1, c - 1);
	}
	now = comb(r, r - 1);
	for (int i = w; i >= z; i--) {
		ans += now * comb(x + i - 1, x - 1);
		now += comb(r + (w - i) + 1, r - 1);
	}
	cout << ans << endl;
	return 0;
}