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;
#define ll long long
#define MOD 1000000007

ll arr[2000050];

ll cal(ll a,int b) {
	if (b==0) return 1;
	if (b%2==1) return a*cal(a*a%MOD,b/2)%MOD;
	else return cal(a*a%MOD,b/2); 
}

ll f(int x,int y) {
	return arr[x+y]*cal(arr[x],MOD-2)%MOD*cal(arr[y],MOD-2)%MOD;
}

ll g(int x,int y) {
	ll sum=0;
	for (int i=1;i<=x+1;i++) (sum+=f(i,y))%=MOD;
	return sum;
}

int main(){  
	int r1, r2, c1, c2;  
	arr[0]=1;
	for (int i=1;i<2000010;i++) arr[i]=(arr[i-1]*(ll)i)%MOD;
	cin>>r1>>c1>>r2>>c2;
	ll ans=g(r2,c2)-g(r1-1,c2)-g(r2,c1-1)+g(r1-1,c1-1);
	ans%=MOD;
	if (ans<0) ans+=MOD;
	cout<<ans;
	return 0;
}
