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 FasterIO ios_base::sync_with_stdio(0);cin.tie(0);cout.tie(0)

typedef unsigned long long ull;
typedef long long ll;
typedef double db;

#define mem(a,x) memset(a,x,sizeof(a))
#define pb push_back
#define ff first
#define ss second
#define mk make_pair
#define pi pair<int,int>
#define vi vector<int>
#define pL pair<ll,ll>
#define vL vector<ll>
#define vp vector<pi>
#define vpL vector<pL>

const int MX=2000000+5; // (R+C+1)
const ll inf=1e16;
const ll mod=1e9+7;

ll bigmod(ll b, ll p)
{
    ll ans = 1;
    for(; p; p>>=1)
    {
        if(p&1) ans = ans * b % mod;
        b = b * b % mod;
    }
    return ans;
}

ll F[MX], IF[MX];

ll nCr(ll n, ll r)
{
    return IF[r] * IF[n-r] % mod * F[n] % mod;
}

void FCT()
{
    F[0] = IF[0] = 1;
    for(int i = 1; i < MX; i++) F[i] = F[i-1] * i % mod;
    for(int i = 1; i < MX; i++) IF[i] = bigmod(F[i], mod-2);
}


ll tableSum(ll r1, ll c1, ll r2, ll c2)
{
    ll sm=0;
    for(int i = r1; i <= r2; i++)
    {
        sm =(sm + nCr(i + c2 + 1, c2))      % mod;
        sm=(sm - nCr(i + c1, c1 - 1) + mod) % mod;
    }
    return sm;
}

int main()
{
    FasterIO;

    FCT();

    ll r1, c1, r2, c2;

    cin >> r1 >> c1 >> r2 >> c2;

    ll sm = tableSum(r1, c1, r2, c2);

    cout << sm << endl;

    return 0;
}