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 <iostream>
#include <vector>
#include <string>
#define rep(i, n)   for(int i = 0; i < (n); i++)
using namespace std;
typedef long long ll;

const ll mod = 1000000000+7;

ll mod_pow(ll a, ll n, ll p){
    if(n == 0)  return 1;
    if(n%2 == 1)    return (a * mod_pow(a, n-1, p)) % p;
    ll t = mod_pow(a, n/2, p);
    return (t*t) % p;
}

ll fact[2000010];
ll invfact[2000010];

ll nCr(ll n, ll r){
    ll ret = fact[n];
    (ret *= invfact[n-r]) %= mod;
    (ret *= invfact[r]) %= mod;
    return ret;
}

int main(){
    ll r1,c1,r2,c2;    cin >> r1 >> c1 >> r2 >> c2;
    for(ll i = 0; i <= 2000009; i++){
        if(!i)  fact[i] = 1;
        else fact[i] = fact[i-1] * i;
        fact[i] %= mod;
        invfact[i] = mod_pow(fact[i], mod-2, mod);
    }
    ll ans = nCr(r2+c2+2, r2+1);
    ans = ans - nCr(r2+c1+1, c1) + mod;
    ans %= mod;
    ans = ans - nCr(r1+c2+1, r1) + mod;
    ans %= mod;
    ans += nCr(r1+c1, r1);
    ans %= mod;
    cout << ans << endl;
}