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 <bits/stdc++.h>
#define f(i,n) for(int i=0;i<n;i++)
#define P pair<int,int>
#define S second
#define mod 1000000007
#define int long long
using namespace std;
int k[2000002];
int mypow(int a, int b, int c) {
	if (b == 0)return 1;
	if (b % 2)return mypow(a, b - 1, c)*a%c;
	int z = mypow(a, b / 2, c);
	return z * z%c;
}
int nCr(int a, int b) {
	if (b < 0 || a < b)return 0;
	return k[a] * mypow(k[a - b], mod - 2, mod) % mod*mypow(k[b], mod - 2, mod) % mod;
}
signed main() {
	int a, b, c, d;
	cin >> a >> b >> c >> d;
	k[0] = 1;
	f(i, c + d + 2) {
		k[i + 1] = k[i] * (i + 1) % mod;
	}
	cout << (nCr(a + b, a) + nCr(c + d + 2, c + 1) - nCr(a + d + 1, a) - nCr(b + c + 1, b))%mod<<endl;
}