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).

Examples

Input

1 1 2 2


Output

14


Input

314 159 2653 589


Output

602215194
#include<cstdio>
#include<iostream>

#define ll long long

using namespace std;

const int MOD = 1e9+7;
const int N = 1e6+10;

int record[2*N];

inline ll pow(ll a,ll b){
	ll res = 1;
	while(b){
		if(b&1)
			res = (res * a) % MOD;
		a = (a * a) % MOD;
		b >>= 1;
	}
	return res;
}

inline ll A(ll a){
	return record[a];
}

inline ll C(ll a,ll b){
	ll res = (A(a) * pow((A(a-b)*A(b))%MOD,MOD-2))%MOD;
	return res;
}

int main(){
	//freopen("in","r",stdin);
	ios_base::sync_with_stdio(false); cin.tie(0);
	record[0] = 1;
	int a,b,c,d; cin >> a >> b >> c >> d;
	for(ll i = 1;i <= 2*N;i++) record[i] = (record[i-1]*i)%MOD; 
	ll res = 0;
	for(int i = a;i <= c;i++){
		res = (res + C(d+i+1,i+1) - C(b+i,i+1) + MOD)%MOD;	
	}	
	cout << res << endl;
}