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: Wrong Answer)

#include <iostream>
#include <cmath>
#include <complex>
#include <string>
#include <sstream>
#include <limits>
#include <algorithm>
#include <functional>

#include <vector>

using namespace std;

const long long MOD = 1e9 + 7;

template<typename value_type>
class fast_combination
{
public:
	value_type mod_value;

	vector<value_type> mod_inv;
	vector<value_type> fact;
	vector<value_type> fact_inv;

public:
	fast_combination(const value_type& limit, const value_type& m)
		: mod_value(m), mod_inv(), fact(), fact_inv()
	{
		mod_inv.assign(limit + 1, 0);
		fact.assign(limit + 1, 0);
		fact_inv.assign(limit + 1, 0);

		mod_inv[1] = 1;
		fact[0] = 1;
		fact[1] = 1;
		fact_inv[0] = 1;
		fact_inv[1] = 1;

		for (value_type i = 2; i <= limit; i++)
		{
			mod_inv[i] = (MOD - (MOD / i) * mod_inv[MOD % i]) % MOD;
			fact[i] = (fact[i - 1] * i) % MOD;
			fact_inv[i] = (fact_inv[i - 1] * mod_inv[i]) % MOD;
		}
	}

public:
	value_type process(const value_type& n, const value_type& r)
	{
		if (n < 0 || r < 0) return 0;
		if (n < r) return 0;

		return (fact[n] * (fact_inv[r] * fact_inv[n - r] % MOD)) % MOD;
	}
};

//fast_combination<long long> fc(N, MOD);
//int result = fc.process(n, r);

int main()
{
	ios::sync_with_stdio(false);
	cin.tie(nullptr);
	cout.tie(nullptr);

	fast_combination<long long> fc(2000100, MOD);

	int r1, c1, r2, c2;
	cin >> r1 >> c1 >> r2 >> c2;

	cout << (fc.process(r2 + 1 + c2 + 1, r2 + 1) - fc.process(r2 + 1 + c1, c1) - fc.process(r1 + c2 + 1, r1) + fc.process(r1 + c1, r1) + 2 * MOD) % MOD << endl;

	return 0;
}