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<bits/stdc++.h>
#define PB push_back
#define MP make_pair
#define F first
#define S second
#define MOD	1000000007
#define int	long long
#define pii pair<int,int> 
#define vi vector<int>
using namespace std;

const int N = 2e6 + 10;

int fac[N], inv[N], invFac[N];

void pre(){
	inv[1] = 1;
	int m = 1e9 + 7;
	for(int i = 2; i < N; i++)
		inv[i] = (m - (m/i)*inv[MOD % i]) % MOD ;
	
	fac[0] = invFac[0] = 1;
	for(int i = 1; i < N; i++){
		fac[i] = fac[i-1] * i % MOD;
		invFac[i] = invFac[i-1] * inv[i] % MOD;
	}	
}

int solve(int x, int y){
	int ans = 0;
	ans = (fac[x+y] * invFac[x] % MOD) * invFac[y] % MOD;
	return ans;
}

int32_t main(){
	pre();
	int x1, y1, x2, y2;
	cin >> x1 >> y1 >> x2 >> y2;
	int ans = (((solve(x2+1,y2+1) - solve(x2+1,y1) - solve(x1,y2+1) + solve(x1,y1)) % MOD + MOD) % MOD);
	cout << ans << endl;

	return 0;
}

