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;
typedef long long ll;
const int N = 1e6 + 10;
const int MOD = 1e9 + 7;
ll d[N];
ll qpow(ll x, ll k) {
    ll r = 1;
    while(k) {
        if(k & 1) r = r * x % MOD;
        k >>= 1;
        x = x * x % MOD;
    }
    return r;
}
ll C(int i, int j) {
    return d[i] * qpow(d[i-j], MOD-2) % MOD * qpow(d[j], MOD - 2) % MOD;
}
ll Cal(int i, int j) {
    ll res = 0;
    // C(i+j, j)
    for(int x = 0; x <= j; x++) {
        res += C(x+i-j+1, x+1);
        res %= MOD;
    }
    return res;
}
int main() {
	d[0] = 1;
    for(int i = 1; i < N; i++) {
        d[i] = d[i-1] * i % MOD;
    }
    int r1, r2, c1, c2;
    cin >> r1 >> c1 >> r2 >> c2;
    ll ans = Cal(r2+c2, c2) - Cal(r1-1+c2, c2) - Cal(r2+c1-1, c1-1) + Cal(r1-1+c1-1, c1-1);
    ans %= MOD;
    ans += MOD;
    ans %= MOD;
    cout << ans << '\n';
}