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;

typedef long long ll;
typedef pair<int,int> P;

#define p_ary(ary,a,b) do { cout << "["; for (int count = (a);count < (b);++count) cout << ary[count] << ((b)-1 == count ? "" : ", "); cout << "]\n"; } while(0)
#define p_map(map,it) do {cout << "{";for (auto (it) = map.begin();;++(it)) {if ((it) == map.end()) {cout << "}\n";break;}else cout << "" << (it)->first << "=>" << (it)->second << ", ";}}while(0)

const ll mod = 1000000007;
//const ll mod = 998244353;

const int MAX_N = 2000020;
ll fact[MAX_N],fact_inv[MAX_N],inv[MAX_N];

ll pow_mod(ll a,ll b) {
    ll ret;
    if (b < 0) ret = pow_mod(a,mod+b-1);
    else if (b == 0) ret = 1;
    else if (b == 1) ret = a;
    else {
        ll c = pow_mod(a,b/2);
        if (b%2) ret = (c*c)%mod*a%mod;
        else ret = c*c%mod;
    }
    return ret;
}

void init(int x) {
    fact[0] = 1;fact[1] = 1;
    for (int i = 2;i <= x;++i) fact[i] = fact[i-1]*i%mod;
    fact_inv[x] = pow_mod(fact[x],-1);
    for (int i = x;i > 0;--i) fact_inv[i-1] = fact_inv[i]*i%mod;
    for (int i = 1;i <= x;++i) inv[i] = fact_inv[i]*fact[i-1]%mod;
}

ll combi(ll a, ll b) {
    return fact[a]*fact_inv[b]%mod*fact_inv[a-b]%mod;
}

int main() {
    ll r1,c1,r2,c2;
    cin >> r1 >> c1 >> r2 >> c2;
    init(2000010);
    cout << (combi(r2+c2+2,r2+1)+combi(r1+c1,r1)-combi(r2+c1+1,r2+1)-combi(r1+c2+1,r1)+mod+mod)%mod << endl;
}