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: Accepted)

#include <bits/stdc++.h>
using namespace std;
#define forloop(n) for(int i = 0; i < n; i++)
#define ll long long
#define mod 1000000007
long long exp(long long taban, long long us) {
    long long carpan = taban;
    long long temp = us;
    long long res = 1;
    for(int i = 0;;i++){
        if(temp % 2) res = (res*carpan) % mod;
        temp /= 2;
        carpan = (carpan*carpan) % mod;
        if(temp == 0) break;
    }
    return res;
}
ll ebob(ll a, ll b){
	if(!a)return b;
	return ebob(b%a, a);
}
ll ekok(ll a, ll b){
	return (((a*b)%mod)*(exp(ebob(a,b), (ll)mod-2))) % mod;
}
/*void set_levels(int cur, int dont){
	level[cur] = level[dont] + 1;
	parent[cur] = dont;
	for(int i = 0; i < vec[cur].size(); i++){
		if(vec[cur][i] != dont) set_levels(vec[cur][i], cur);
	}
}*/
ll fact[2000005];
ll komb(ll a, ll b){
	a++;
	ll payda = (fact[a]*fact[b]) % mod;
	return (fact[a+b] * (exp(payda, mod - 2))) % mod;
}

int main(){
	ios_base::sync_with_stdio(false); cin.tie(NULL);
	ll r1, c1, r2, c2; cin>>r1>>c1>>r2>>c2;
	fact[0] = 1;
	for(ll i = 1; i < 2000005; i++){
		fact[i] = fact[i-1] * i % mod;
	}
	ll res = 0;
	ll u = 0;
	for(ll i = min(r1, r2); i <= max(r1, r2); i++){
		res += komb(i, max(c1,c2));
		res -= komb(i, min(c1,c2)-1);
		if(res < 0) res += mod;
		res %= mod;
	}
	//(r, r)..(r+n, r) -> (r+n+1, r+1);
	//(r, r)..(r+m, r)
	cout<<res;
}