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>

using namespace std;

int main(){
	ios_base::sync_with_stdio(false);
	cin.tie(NULL);
	
	int r1,r2,c1,c2;
	cin >> r1 >> c1 >> r2 >> c2;
	
	long long mod=1000000007;
	
	int fs=2050502;
	vector<long long> fact(fs),ifact(fs),invs(fs);
	fact[0]=ifact[0]=fact[1]=ifact[1]=invs[1]=1;
	for(int i=2;i<fs;i++){
		fact[i]=fact[i-1]*i%mod;
		invs[i]=mod-invs[mod%i]*(mod/i)%mod;
		ifact[i]=ifact[i-1]*invs[i]%mod;
	}
	function<long long(int,int)> binom=[&](int a,int b){
		if(b==0) return 1LL;//
		if(a<b || b<0) return 0LL;
		return fact[a]*ifact[b]%mod*ifact[a-b]%mod;
	};
	
	long long res=0;
	for(int i=c1;i<=c2;i++){
		res=(res+binom(r2+i+1,r2)-binom(r1+i,r1-1)+mod)%mod;
	}
	cout << res << "\n";
	return 0;
}