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 int long long
#define f first
#define s second
using namespace std;
const int N=3000009,mod=1e9+7;
	int f[N],iv[N];
int pw(int a,int t=mod-2){
	int x=1;
	while(t){
		if(t&1)x=x*a%mod;
		a=a*a%mod,t>>=1;
	}
	return x;
}
int C(int n,int r){
	int x=(((f[n]*iv[r])%mod)*iv[n-r])%mod;
	return x;
}
int32_t main(){
	if(fopen("input.txt", "r"))
		freopen("input.txt", "r", stdin),
		freopen("output.txt", "w", stdout);
	ios::sync_with_stdio(0),cin.tie(0);
	f[0]=1,iv[0]=1;
	for(int i=1;i<N;i++){
		f[i]=i*f[i-1]%mod;
		iv[i]=pw(f[i]);
	}
	int r1,r2,c1,c2,sum=0;
	cin >> r1 >> c1 >> r2 >> c2;
	for(int i=c1;i<=c2;i++)
		sum=(sum+(C(r2+i+1,r2)+mod-C(r1+i,r1-1)))%mod;
	cout << sum;

}