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: Runtime Error)

#include <bits/stdc++.h>
using namespace std;

const int _n = 1e5 + 10;
vector<int> Fact(_n), Inv(_n);
const int kmod = 1000000007;

int mul(int a, int b, int mod = kmod)
{
    return (long long) a * b % mod;
}

int add(int a, int b, int mod = kmod)
{
    a += b;
    if (a >= mod)
        a -= mod;
    return a;
}

int sub(int a, int b, int mod = kmod)
{
    a -= b;
    if (a < 0)
        a += mod;
    return a;
}

int power(int base, int index, int mod = kmod)
{
    if (index == 0)
        return 1;
    int temp = power(base, index / 2, mod);
    temp = mul(temp, temp, mod);
    if (index & 1)
        temp = mul(temp, base, mod);
    return temp;
}

void pre()
{
    Fact[0] = 1;
    for (int i = 1; i < _n; ++i)
        Fact[i] = mul(Fact[i - 1], i);
    Inv[_n - 1] = power(Fact[_n - 1], kmod - 2);
    for (int i = _n - 2; i >= 0; --i)
        Inv[i] = mul(Inv[i + 1], (1 + i));
}

int ncr(int n, int r)
{
    if (n < 0 || r < 0 || n - r < 0)
        return 0;
    return mul(Fact[n], mul(Inv[r], Inv[n - r]));
}

int main(){

    
    int r1,r2,c1,c2;
    cin>>r1>>c1>>r2>>c2;
    
    long long  sum = 0,x,p,q;
    
    pre();
    
    for(long long i=0;i<=c2-c1;i++){

        for(long long j=0;j<=r2-r1;j++){
            
            sum = add(sum,ncr(r1+c1+i+j,r1+j));
        }
    }
    
    cout<<sum<<endl;
    
    return 0;
}